HOW  WE  LBARN 


SHORT  PRIMER  OF  SCIENTIFIC 
METHOD  FOR  BOYS 


W.  H.S.JONES 


PRICE  ONE  SHILLING  AND  SIXPENCE 


CAMBRIDGE 


Ex  Libris 
C.  K.  OGDEN 


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HOW    WE    LEARN 


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HOW    WE    LEARN 

A    SHORT    PRIMER    OF   SCIENTIFIC 
METHOD    FOR    BOYS 


BY 

W.    H.   S.   JONES,    M.A. 

Fellow  and  Lecturer  of  St  Catharine's  College 

Senior  Classical  Master  at  the  Perse  School 

Cambridge 


Cambridge  : 

at  the  University   Press 
1916 


TO  THE  MEMORY 
OF 

S.  S.  F.  F. 


LB 


PREFACE 

THIS  little  book  is  intended  for  the  use  of  scholars 
of  about  sixteen,  who  for  some  terms  at  least  have 
been  trained  to  work  out  exercises  in  induction  of  the 
kind  described  and  illustrated  in  the  pamphlet  Scientific 
Method  in  Schools.  It  sums  up  and  systematizes,  and 
to  a  certain  extent  develops,  what  they  have  been 
learning  incidentally  and  partially.  But  it  contains 
the  very  minimum  that  a  pupil  of  sixteen  should  know, 
and  it  is  suggested  that  the  teacher  would  do  well, 
before  setting  a  section  to  be  studied  and  learned 
at  home,  first  to  give  an  oral  lesson  expanding  and 
illustrating  the  points  treated  in  that  section.  The 
exercises  at  the  end  are  intended  to  serve  as  written 
home  work. 

I  hope  that  nobody  will  be  offended  at  my  inten- 
tional medley  of  trivial  and  important,  of  commonplace 
decisions  and  momentous  discoveries.  Such  mixtures 
should  not  appear  incongruous  to  anyone  who  remem- 
bers that  "the  method  of  discovery"  is  essentially  one. 
MVIy  main  object  has  been  to  impress  upon  the  learner 
the  unity  of  knowledg^ 

The  teacher  may  find  it  useful  if  I  append  here 
a  short  list  of  problems  that  can  be  worked  out  by 
teacher  and  class  together  during  the  preparatory 
years  before  this  primer  is  studied.  The  main  charac- 
teristic of  this  work  should  be  scientific  thoroughness, 


iOS^6i38 


vi  Preface 

and  the  way  of  conducting  it  is  described  at  some 
length  in  the  pamphlet  mentioned  above.  Some  of 
these  problems  can  be  worked  out  by  brighter  and 
older  pupils  without  help,  but  the  teacher  ought  to  be 
careful  not  to  encourage  unscientific  habits  by  setting 
tasks  above  the  powers  of  the  class. 

Exercises  est  Induction  for  Pupils  between 
the  ages  of  13  and  16. 

(1)  Definitions  of  ordinary  terms;  e.g.,  stupidity, 
hurry,  piety,  food,  despair,  sultriness,  remorse,  rapacity, 
statesman,  quibble,  pilgrim,  drug,  distress,  instrument, 
Iward,  harangue. 

(2)  Grammar  rules  of  various  languages;  e.g.,  the 
use  of  which  and  who  in  modem  Enghsh ;  the  differ- 
ence between  le  and  lui  in  French ;  the  rules  for  the 
agreement  of  the  relative  in  Latin;  the  use  of  the 
subjunctive  in  Latin  to  express  indirect  command ; 
the  rules  for  the  agreement  of  the  participle  in  French  ; 
the  use  of  the  supine  in  Latin. 

(3)  Historical  commonplaces,  e.g.,  the  value  of 
sea  power ;  the  value  of  strong  government,  even  if 
tyrannical ;  the  economic  factor  as  a  cause  of  wars ; 
the  dangers  of  absolute  monarchy ;  oratory  as  a  force 
in  history ;  the  factors  most  favourable  to  the  growth 
of  democrac3^ 

(4)  Mountain  barriers  as  a  protection  from  enemies ; 
the  origins  of  lakes;  why  to^ns  have  dwindled  or 
disappeared ;  the  effects  of  rivers  upon  the  history  of 
those  dwelling  in  their  basins ;  "the  rule  of  the  isthmus  " 
in  ancient  times ;  the  influence  of  large  deserts  upon 
surrounding  countries. 


Preface  vii 

(5)  The  law  of  levers ;  the  law  of  pulleys ;  to 
find  the  centre  of  gravity  of  a  disc,  cube,  etc. ;  the 
scientific  meaning  of  "burning";  heat  and  expansion; 
elements  combine  in  fixed  proportions  by  weight  (a 
working  hypothesis  formed  from  a  few  illustrations  of 
the  law) ;   the  effect  of  darkness  upon  plants. 

(6)  The  marks  generally  left  upon  a  man  by  his 
trade  or  profession  (cobbler,  farmer,  fisherman,  engineer, 
etc.) ;  how  to  detect  a  smoker,  a  consumptive  man,  a 
short-sighted  man,  a  man  with  a  weak  heart;  the 
chief  symptoms  of  common  ailments. 

I  must  thank  Mr  W.  E.  Johnson,  Fellow  of  King's 
College,  Professor  R.  L.  Archer  and  Mr  F.  W.  Westaway, 
for  their  great  kindness  in  reading  the  proofs  and  cor- 
recting many  errors  and  ambiguities. 

W.  H.  S.  J. 

September  1916. 


CONTENTS 


CHAPTER   I 

PAGE 

Introductoby 1 


CHAPTER   II 
Words  and  theib  Meanings      .        .  8 

CHAPTER  III 
SoLENTiric  Method       .        .        .        .        19 

Additionax  Note          .        .        .        .        51 

APPENDIX 

Examples  of  Inductive   Reasoning 

DONE  BY  Boys        ....        52 

Questions 60 


CHAPTER   I 

INTRODUCTORY 

Knowledge  and  Sensation. 

What  is  Truth?  What  is  Knowledge?  Philo- 
sophers and  scientists  have  discussed  these  questions 
for  well  over  two  thousand  years,  but  complete  answers 
seem  as  remote  as  ever.  There  has,  however,  been 
great  progress,  particularly  during  the  last  three 
hundred  years.  The  problems  are  not  solved,  but  we 
see  our  way  better,  and  realize  that  we  are  on  the  right 
road  to  the  solution,  even  though  it  prove  ultimately 
to  be  unattainable.  It  is  with  the  certainties,  the 
admitted  facts,  that  this  little  book  will  deal.  Kl  wish 
to  point  out  how  each  one  of  us  can  make  his  thoughts 
more  accurate,  and  so  express  them  that  they  may  be 
accurately  communicated  to  others.) 

Pause  for  a  moment  and  try  to  examine  the  nature 
of  your  thoughts,  the  contents  of  your  consciousness, 
the  way  in  which  your  mind  acts  upon  the  sensations 
presented  to  it. 

In  your  waking  hours  a  continuous  stream  of  im- 
pressions intrudes  itself  upon  you,  impressions  of  shape, 
colour,  smell,  taste,  touch,  sound — everything  in  fact 

J.  1 


2  Introductory 

that  is  conveyed  by  the  five  senses — the  meaning  of 
which,  in  proportion  to  the  activity  of  your  brain,  you 
try  to  make  clear  to  yourself.  If  you  are  sleepy, 
inattentive  or  ill,  the  impressions  are  often  unobserved. 
The  remark  is  constantly  heard,  "I  did  not  notice 
that."  But  for  the  most  part  your  mind  is  acting  as 
an  interpreter,  explaining  and  arranging  your  sensa- 
tions.    You  say  to  yourself: — 

That  is  a  horse. 

The  rain  falls  fast. 

The  church  is  round. 

A  bell  is  ringing. 
These  and  similar  statements  are  all  interpretations 
of  sense-impressions. 

But  the  powers  of  the  mind  are  not  limited  to 
present  sensations  and  their  interpretation.  It  can 
store  up  experience,  a  power  we  call  memory,  and 
so  pass  judgment  on  the  past;  it  can  also  look 
forward  and  prophesy  about  the  future. 

There  was  a  frost  last  week. 

X.  made  fifty  runs  this  afternoon. 

Julius  Caesar  was  a  great  Roman. 

We  shall  go  to  London  to-morrow. 

There  will  be  a  shower  soon. 
A  close  examination  reveals  that  the  powers  of  the 
mind  are  conditioned  by  its  past  experience,  in  the 
light  of  which  it  works.  This  experience  may  be  its 
own.  It  may,  however,  be  the  experience  of  other 
minds,  passed  on  by  one  of  the  means  we  possess  of 
transmitting  thought.  The  character  of  Julius  Caesar, 
for  example,  is  known  to  us  because  we  have  accounts 
of  him  in  writing,  which  preserve  for  us  the  thoughts 
of  Caesar's  contemporaries. 


Introductory  3 

But  even  the  simplest  acts  of  thought  about  present 
sense-impressions  imply  experience.  Let  us  take  the 
sentence : — 

That  is  an  orange. 

What  are  our  sense-impressions?  We  see  some- 
thing yellow,  that  looks  round.  If  that  were  all 
we  might  be  uncertain  whether  it  is  an  orange  or  a 
yellow  ball.  But  if  we  handle  the  yellow  thing  we 
are  enabled  to  come  to  a  correct  decision.  Experience 
comes  to  our  aid  and  tells  us  that  balls  do  not  "feel" 
quite  so.  Furthermore,  the  mere  use  of  language,  with- 
out which  we  cannot  think  to  any  great  extent,  implies 
experience.  When  I  read,  either  to  myself  or  aloud,  the 
word  horse,  I  immediately  associate  the  sound  with 
a  kind  of  composite  photograph  in  my  mind  which  has 
been  formed  by  a  long  succession  of  past  sense-impres- 
sions, each  one  of  which  I  have  learnt  to  associate  with 
the  word.  Kangaroos  I  have  never  seen,  but  the  name 
suggests  to  me  pictures  and  descriptions  all  of  which 
appeal  to  my  own  sense-experience. 

The  material,  then,  with  which  mind  works  can  be 
analysed  into  sense-impressions,  which  it  interprets 
and  stores  up  in  what  we  call  experience.  Countless 
individuals  have  added  to  this  stock  of  experience,  and 
made  it  accessible  to  others  by  means  of  language, 
whether  oral  or  written.  The  mind  works  by  giving 
a  meaning  to  these  sense-impressions,  by  interpreting 
them,  by  explaining  their  relations  one  to  another — 
in  brief,  by  bringing  order  and  system  to  what  would 
otherwise  be  a  meaningless  chaos  like  the  appearances 
in  certain  kinds  of  dreams. 

This  attention  to  order  and  system  is  the  chief 
characteristic  of  knowledge  or  science.     The  scientist 

1—2 


4  Thoughts  are  Judgments 

aims  at  building  out  of  the  vast  mass  of  human  experi- 
ence an  orderly  whole,  wdth  its  parts  duly  and  properly 
connected,  an  organized  unity,  a  universe.  So  large  is 
the  material  that  few  scientific  men  live  long  enough 
to  do  more  than  to  arrange  a  very  few  facts,  thus 
bringing  nearer  to  completion  a  tiny  portion  of  the  huge 
building.  But  the  workers  are  diligent  and  numerous. 
Bit  by  bit,  little  by  little,  the  edifice  progresses,  and 
though  we  cannot  yet  see  signs  when,  if  ever,  it  will 
be  completed,  we  must  be  content  with  the  thought 
that  each  day  registers  an  advance  upon  the  preceding. 

Thoughts  are  Judgments. 

But  we  must  return  to  our  examination  of  thought. 
Whenever  we  interpret  our  sense-impressions,  whenever, 
in  fact,  we  really  think,  we  are  as  it  were  pronouncing  a 
verdict.     A  thought  is  a  judgment : — 

This  tea  is  too  sweet  for  me. 

The  train  is  on  the  move. 

A  cup  is  standing  on  the  table. 
All  these  sentences  are  expressions  of  a  verdict,  and 
represent  a  decision  reached  by  the  mind.  Now  a 
judgment  of  necessity  imphes  two  things  between  which 
a  relation  is  declared  to  exist.  The  three  sentences 
given  above  may  thus  be  divided  into  their  constituent 
parts : — 

This  tea  |  over-sweetness. 

The  train  |  movement. 

Cup  I  position  on  the  table. 


The  Testing  of  Judgments  5 

The  Testing  of  Judgments. 

How  can  we  be  sure  that  the  connections  are 
rightly  made,  that  the  verdicts  are  true  and  the  judg- 
ments correct? 

In  some  cases  we  cannot  prove  the  correctness  at  all. 
If  I  find  the  tea  too  sweet,  no  amount  of  argument,  no 
demonstration  that  only  one  small  lump  was  put  into 
the  cup,  will  induce  me  to  alter  my  decision.  I  alone 
am  a  competent  judge  of  my  likes  or  dislikes.  As  to 
the  motion  of  the  train,  I  am  ready  to  admit  that  my 
eyes  may  have  deceived  me,  and  if  a  number  of  by- 
standers deny  my  statement  I  shall  probably  acquiesce. 
Another  person's  judgment  in  such  cases  is,  given 
equally  good  eyesight  and  equally  good  opportunities 
of  observation,  as  lU^ely  to  be  correct  as  mine.  Simi- 
larly in  the  case  of  the  cup  and  the  table.  The  evidence 
of  better  observers  or  a  closer  inspection  on  my  own 
part  may  possibly  lead  me  to  conclude  that  it  is  not  a 
cup  but  a  mug,  not  a  standing  position  but  a  lying 
position,  not  a  table  but  a  sideboard.  These  cases  are 
simple,  and  not  likely  to  cause  any  difficulty.  But 
often  the  greatest  care  is  necessary  in  testing  a  judg- 
ment. How  to  do  so  accm-ately  we  learn  by  studying 
logic  and  scientific  method.  We  must  now  distinguish 
between  them.  Strictly  speaking,  logic  deals  with  the 
rules  to  be  observed  during  the  process  of  reasoning. 
If  certain  assumptions  are  made,  logic  tells  us  what 
conclusion  we  can  legitimately  draw  from  them.  It 
does  not  concern  itself  with  the  truth  or  falsity  of 
the  assumptions,  but  only  with  the  proper  way  for 
thought  to  deal  with  any  material  that  is  put  before  it^. 

^  I  use  logic  in  the  sense  oi  formal  logic. 


6  The  Testing  of  Judgments 

Logic  has  no  fault  to  find   with  the  following   argu- 
ment : — 

All  butterflies  have  a  thousand  legs. 

This  creature  is  a  butterfly. 

Therefore  this  creature  has  a  thousand  legs. 
The  reasoning  is  quite  vahd,  and  logic  does  not 
grumble.     But  logic  is  far  from  contented  if  we  say: — 

All  men  have  two  legs. 

This  creature  has  two  legs. 

Therefore  this  creature  is  a  man. 
The  creature  maj'  be  a  man,  but  the  argument  does 
not  prove  it.  The  reasoning  is  not  valid,  for  although 
all  men  have  two  legs,  aU  two-legged  creatures  are 
not  necessarily  men.  Some  are  monkeys.  Scientific 
method,  on  the  other  hand,  although  it  makes  use  of 
logic,  is  not  content,  as  logic  is,  to  take  statements  for 
granted.  It  compares  statements  with  reality.  It 
examines  butterflies,  and  shows  by  observation  that 
they  have  not  a  thousand  legs.  It  examines  the 
creature  with  two  legs,  and  by  comparison  and  contrast 
shows  that  it  is  not  a  man  but  a  goriUa.  Scientific 
method,  in  fact,  includes  logic  but  goes  beyond  it  by 
insisting  that  the  judgments  with  which  logic  deals 
shall  correspond  to  reahty,  the  nature  of  which  it  tries 
to  apprehend  with  ever-increasing  clearness,  using 
logic  as  one  means  to  that  end. 

Grammar. 
It  will  be  convenient  here  to  pay  a  little  attention 
to  the  meaning  of  the  word  grammar.  Grammar  is 
the  science  of  words.  Now  it  is  by  means  of  words,  or 
language,  that  we  express  our  thoughts  or  judgments. 
In  so  far  as  they  both  are  concerned  with  thoughts 


Grammar  7 

there  is  a  close  connection  between  grammar  and  logic. 
The  fundamental  parts  of  a  sentence,  the  subject  and 
predicate,  correspond  roughly  to  the  two  components 
which  are  united  by  our  minds  when  we  make  judg- 
ments. There  are  other  points  in  which  logic  and 
grammar  correspond.  But  language,  which  is  the 
subject  of  grammar,  expresses  not  only  our  judgments 
but  our  feelings  or  emotions.  Man  is  not  entirely  a 
rational  creature,  and  his  language  often  betrays  the 
fact.  Furthermore,  language  is  at  best  an  imperfect 
instrument,  and  the  logical  connection  of  our  thoughts 
is  often  implied  instead  of  being  explicitly  stated.  You 
must  remember  that  grammatical  accuracy  is  merely 
conformity  with  the  ways  in  which  educated  people 
use  words ;  logical  accuracy  is  conformity  with  the  laws 
of  valid  reasoning.     The  sentences  given  above: — 

All  men  have  two  legs; 

This  creature  has  two  legs; 

Therefore  this  creature  is  a  man; 
are  all  quite  grammatical.     You  can  parse  and  analyse 
them  without  finding  any  flaw.     Logically,  however, 
the    argument    is    unsound.     Remember,    then,    that 
grammar  deals  with  words,  logic  with  thoughts. 


CHAPTER   II 

Words  and  their  Meanings. 

When  a  little  child  is  learning  to  speak  he  at  first 
attaches  to  a  sound  the  vaguest  of  meanings.  Any 
kind  of  building  is,  for  him,  a  house;  anything  that 
causes  pleasure  is  nice.  As  time  goes  on,  sense-im- 
pressions are  interpreted  more  accurately,  and  a  more 
accurate  use  of  words  is  the  result.  But  perfect  pre- 
cision in  the  use  of  language  is  never  attained  by 
anybody;  it  is  therefore  all  the  more  necessary  for  us 
consciously  to  exercise  ourselves  in  fixing  what  mean- 
ings words  suggest  to  om*  minds.  There  is  especial 
need  of  care  in  deahng  with  words  that  denote  abstrac- 
tions, such  Si's,  justice,  courage,  wit,  cruelty,  or  with  words 
that  represent,  not  nature's  classes  {horse,  cat,  butterfly) 
but  human  inventions,  e.g.,  State,  republic,  politician, 
table,  machine.  You  must  remember  that  the  meaning 
which  a  person  assigns  to  a  word  depends  in  no  small 
degree  upon  his  owti  experience.  He  cannot  help 
associating  vAth  a  word  all  that  he  has  suffered  or 
enjoyed  from  the  person  or  thing  denoted  by  it.  If  a 
boy's  father  be  habitually  unkind  or  cruel,  that  boy 
will  also  be  tempted  to  associate  the  word  father  %\dth 
unpleasant  memories  of  harsh  treatment.     He  must 


Words  and  their  Meanings  9 

therefore  be  continually  on  his  guard  against  this 
tendency,  and  try  to  assimilate  his  notion  of  a  father 
to  that  formed  by  the  more  fortunate  majority  of 
children.  It  is  because  words  thus  sum  up  the  past 
experience  of  an  individual  that  perfect  uniformity  of 
meaning  is  impossible.  I  often  cannot  avoid  mis- 
understanding my  neighbour  because  his  use  of  words 
is  not  quite  the  same  as  my  own.  But  however 
impossible  it  is  always  to  understand  fully  what  is  said 
to  us,  we  must  never  cease  to  make  the  effort.  Above 
all,  we  must  try  to  take  away  from  the  meanings  we 
attach  to  words  that  which  is  pecuUar  to  ourselves, 
being  due  to  the  singularities  of  our  own  experience. 
Otherwise  we  inevitably  fall  into  confusion,  error  and 
futile  disputes.  How,  then,  is  it  possible  to  use  words 
with  greater  precision?  How  do  we  learn  to  speak 
more  accurately  ?  I  refer,  of  coiurse,  not  to  grammatical 
accuracy,  but  to  that  accuracy  which  consists  in  putting 
the  right  labels  (I  mean  words)  to  the  things  around  us. 
Linguistic  accuracy  generally  accompanies  accuracy  of 
observation  and  of  thought.  As  we  learn  to  distinguish 
a  thing  from  something  else  like  it,  we  learn  also  to 
name  that  thing  properly.  As  you  learn  about  moths 
you  want  names  to  give  to  the  different  kinds,  and  as 
your  knowledge  increases  you  use  these  names  with 
fewer  mistakes.  Correct  classification,  in  fact,  is  of 
immense  importance,  being  the  foundation  of  scientific 
knowledge.  Animals  and  things  are  nearly  all  capable 
of  being  grouped.  Some  groups  exist  naturally ;  others 
are  artificial,  man-made,  and  therefore  far  more 
irregular  than  the  former.  It  is  very  difficult,  for 
instance,  to  know  exactly  what  is  meant  by  a  Conser- 
vative.    Conservatives  form   an   artificial  group,   and 


10  Definitions 

the  views  of  its  members  are  not  fixed,  but  are  sure  to 
dififer,  to  some  extent  at  least,  from  period  to  period. 
For  this  reason  it  is  hard,  if  not  impossible,  to  define 
Conservatives.  The  most  that  can  be  done  is  to  state 
the  general  tendency  of  Conservative  poUcy,  to  enu- 
merate the  characteristics  which  have  been  common 
to  Conservatives  of  all  periods. 

Definitions. 

Words  denoting  abstractions,  or  which  have  a 
vague  or  fluctuating  meaning,  such  as  courage,  republic, 
Liberal,  Church,  always  tend,  in  some  minds  at  any  rate, 
to  become  mere  names  unconnected  with  reahty.  So 
powerful  is  the  spell  exercised  by  words  that  we  are 
inclined  to  think  that  we  have  only  to  be  familiar  with 
a  name  to  be  famihar  also  with  the  thing  the  name 
represents.  The  best  corrective  to  this  fallacy  is  the 
habit  of  framing  definitions.  As  soon  as  we  realize 
that  a  word  is  but  a  label,  a  convenient  reminder  of  a 
person,  thing  or  group,  it  becomes  plain  at  once  why 
it  is  important  never  to  allow  the  connection  between 
word  and  reaUty  to  be  broken.  Only  some  parts  of 
reahty,  however,  admit  of  true,  logical  definition. 
Individual  persons  and  things  cannot  be  defined, 
neither  can  certain  of  the  most  general  kinds  of  reahty. 
We  cannot  define  Napoleon  ;  neither  can  we  define 
being  or  substance.  Definitions  are  properly  of  species, 
which  can  be  defined  by  taking  the  class  above  and 
then  adding  the  special  characteristics  which  distin- 
guish the  species  we  have  in  mind  from  the  other 
species  belonging  to  the  same  higher  class,  or  genus 
as  it  is  called.     Thus  portraits  {species)  are  pictures 


Definitions  1 1 

{genus)  of  real  persons  or  animals  {specific  characteristic). 
I  have  used  the  words  "class,"  "genus,"  "species," 
in  their  ordinary,  everyday  sense,  but  scientists  use 
special  names  when  referring  to  the  classes  of  hving 
things.  Thus  tigers  are  the  species  Felis  tigris,  of 
the  genus  Felis,  of  the  family  FeUdae,  of  the  order 
Carnivora,  of  the  series  Vertebrata.  The  classes  are 
subdivided,  and  divisions  tend  to  shade  into  their 
neighbours.  In  fact  the  classification  is  more  a  matter 
of  convenience  than  of  strictly  scientific  accuracy, 
and  the  great  work  of  Charles  Darwin  was  to  show  how 
a  new  species  develops  out  of  an  old  one.  Neverthe- 
less this  method  of  classification  enables  us  to  define 
natural  classes  more  easily  and  more  accurately  than 
any  other. 

It  is  now  clear,  I  think,  why  only  classes,  and  of 
these  not  the  highest,  can  be  defined.  Only  a  class 
other  than  the  highest  can  be  equated  with  a  part  of 
a  higher  class  possessing  characteristic  qualities  which 
mark  it  off  from  the  rest  of  that  higher  class. 

A  very  good  way  of  defining  a  class  which  is  not 
biological  is  to  examine  carefully  the  synonyms  of  the 
word  used  to  denote  it.  For  example,  suppose  we  wish 
to  define  stupidity.  This  word  has  many  synonyms,  or 
words  meaning  nearly  the  same  thing.  Very  few,  if 
any,  synonyms  have  exactly  the  same  meaning.  The 
synonyms  that  suggest  themselves  are,  among  others, 
foolishness,  silliness,  idiocy  and  dulness.  We  see  at 
once  that  there  is  a  general  similarity  in  the  ideas  these 
words  call  to  our  minds.  They  all  suggest  irrational 
conduct,  or  a  condition  of  mind  leading  to  such  conduct. 
But  irrational  conduct  exhibits  many  variations.  We 
must  try,  by  examining  sentences  in  which  the  synonyms 


12  P^'ecision  of  Speech 

are  correctly  used,  to  discover  the  special  varieties  of 
unreason  they  represent.  We  must  further  remember 
carefully  that  what  we  are  in  search  of  is  not  our  notion 
of  stupidity,  silliness,  and  so  on,  but  the  meanings 
attached  to  these  words  by  the  generaUty  of  mankind. 
It  will  probably  be  decided  that  by  silliness  is  meant 
unreason  caused  by  weakness  of  intellect;  idiocy  is 
unreason  that  reminds  one  of  the  actions  of  certain 
kinds  of  madmen;  foolishness  is  the  unreason  that 
results  from  allowing  one's  brain  to  be  clouded  by  care- 
lessness ;  dulness  is  failure  to  perceive  what  the  ordinary, 
rational  mind  easily  perceives.  Stupidity  is  excess  of 
dulness. 

Precision  op  Speech. 

The  habit  of  using  words  in  precisely  their  right 
meanings  is  well  worth  cultivating,  as  it  leads  to  accuracy 
of  thought  and  lessens  the  risk  of  misunderstandings. 
It  is  one  which  can  be  formed  only  by  very  slow  degrees, 
and  this  fact  is  one  reason,  perhaps  the  chief  reason, 
why  so  few  people  acquire  it.  A  long  and  wide  experi- 
ence, unceasing  vigilance,  close  attention  and  acute 
observation  are  all  necessary,  and  combined  with  these 
quaHties  there  must  be  a  strong  desire  to  improve.  To 
know  the  chief  difficulties  and  dangers  is  of  great  use. 
We  must  learn  to  discriminate  between  synonyms,  to 
discover  the  exact  meanings  attached  to  words  by  the 
best  authors,  to  remember  that  some  words  have  a 
technical  sense,  to  realize  that  a  great  many  words 
slowly  but  surely  change  their  meanings,  and  that  care 
is  required  in  the  use  of  metaphor.  The  last  three 
points  I  will  explain  more  fully. 


Precision  of  Sjyeech  13 

Every  science  has  its  own  terminology,  or  technical 
terms.  These  are  often  borrowed  from  the  language 
of  ordinary  life,  and  so  a  risk  of  confusion  may  arise. 
For  example  we  use  the  word  idea  to  denote  an  opinion, 
but  psychologists  mean  by  the  word  a  general  concep- 
tion formed  in  the  mind  by  a  series  of  experiences. 
Thus  they  speak  of  the  idea  of  justice,  meaning  by 
that  the  general  notion  of  fairness  that  gradually  grows 
in  our  minds  as  the  result  of  coming  into  contact  with 
our  fellow  men.  Whenever  occasion  calls  for  it  care 
should  be  exercised,  and  we  should  ask  ourselves,  "Is 
this  word  used  in  its  ordinary  or  in  its  technical  sense  ?" 
Then  again,  a  word  often  changes  its  meaning.  The 
word  nice,  for  example,  used  to  mean  exact ;  it  now 
means,  in  popular  speech  at  least,  pleasant.  Science 
used  to  mean,  and  still  sometimes  means,  any  know- 
ledge, but  it  seems  to  be  gradually  narrowing  its  mean- 
ing to  knowledge  of  material  forces.  These  are  but 
two  instances  out  of  very  many,  but  they  suffice  to 
make  the  point  clear. 

All  languages  show  a  fondness  for  metaphor, 
although  some  languages  accept  them  more  readily 
than  others.  A  metaphor  is  a  compressed  simile  or 
comparison.  When  we  speak  of  a  "brilliant  achieve- 
ment," we  use  the  word  brilliant,  which  really  means 
shining  brightly,  in  a  metaphorical  sense.  We  are  in 
fact  tacitly  comparing  a  deed  to  a  bright  light.  This 
manner  of  speaking,  while  conducing  to  attractiveness 
of  style  and  often  succeeding  in  giving  to  the  reader  a 
distinct  impression  when  non-metaphorical  language 
would  give  no  impression  at  all,  is  apt  to  detract  from 
scientific  accuracy  of  expression.  Metaphors  must 
always  be  used  with  care.     Perhaps  a  strange,  really 


14  Precision  of  Speech 

startling  metaphor  is  less  deceptive  than  one  which 
has  been  in  use  so  long  that  it  is  almost  worn  out  and 
not  a  true  metaphor  at  aU.  It  is  the  confusing  of 
Uteral  meaning  with  figurative  meaning  which  is  likely 
to  cause  mistakes,  and  the  more  unusual  the  metaphor 
the  less  the  UkeUhood  of  this  confusion  occurring.  If  it 
be  said  that  a  certain  rebel  raised  the  standard  of  revolt 
in  Yorkshire  it  may  reasonably  be  doubted  whether 
he  actually  raised  a  standard  or  whether  he  merely 
started  a  rebelhon  in  that  county.  But  if  I  call  a 
cricketer  a  tower  of  strength  to  his  side,  no  such  possi- 
bihty  of  error  arises.  A  safe  rule  is  never  to  use  a 
metaphor  that  may  give  rise  to  any  reasonable  doubt, 
and  never  to  pass  by  a  possible  metaphor  without 
making  sure,  if  we  can,  that  the  word  or  phrase  is  not 
to  be  taken  in  its  Uteral,  non-metaphorical  sense.  Of 
course  aU  that  I  have  said  applies  only  to  writing  in 
which  strictly  scientific  accuracy  is  essential.  Poetry 
and  prose  appealing  to  the  emotions  and  to  the  aesthetic 
sense  must  be  judged  by  different  rules,  with  which  this 
book  does  not  pretend  to  deal. 

VniTTjES  AND  Defects  of  Language. 

The  usefulness  of  language  is  best  seen  by  consider- 
ing how  we  should  express  our  thoughts  if  men  were 
not  endowed  with  the  power  of  speech.  We  should  be 
confined  to  gesture  and  facial  expression.  These  would 
be  fairly  efficient  ways  of  shomng  what  we  feel,  but 
even  when  practice  had  developed  our  skill  to  the 
utmost  they  would  very  imperfectly  represent  what  we 
think.  Details,  finer  shades  of  meaning,  abstractions 
and  generalizations  could  scarcely  be  expressed  at  all, 


Virtues  and  Defects  of  Language  15 

and  constant  mistakes  and  misconceptions  would  be 
inevitable.  Moreover,  progress  would  be  painfully 
slow,  and  all  the  arts  and  sciences  would  languish,  for 
language  not  only  expresses  thought  but  also  helps  it 
to  a  degree  that  is  difficult  to  reahze.  The  two  pro- 
cesses, in  fact,  of  thinking  and  speaking  (including  of 
course  speaking  silently  to  ourselves)  are  so  closely 
connected  that  they  have  become  almost  one.  So 
powerful  an  instrument  is  speech  that  man,  the  only 
animal  endowed  with  it,  has  been  able,  largely  by  means 
of  its  help,  to  raise  himself  to  a  height  far  above  all 
the  others.  We  must  remember  also  that  a  permanent 
record  of  speech  has  been  discovered  in  writing,  which 
has  preserved  for  us  such  a  vast  amount  of  human 
experience  which  would  otherwise  have  perished,  there- 
by enabling  knowledge  to  accumulate,  and  science  to 
advance  at  a  rapid  rate. 

The  chief  weaknesses  of  language  are : — 

(1)  It  imperfectly  represents  the  emotions. 

(2)  The  meanings  of  words  are  largely  subjective, 
that  is,  words  mean  one  thing  to  one  man  and  another 
thing  to  another  man. 

(3)  Words  tend  to  remain  fixed,  while  the  things 
which  they  represent  tend  to  change. 


Conclusion. 

Language  is  in  spite  of  its  great  utility  an  imperfect 
means  of  expressing  the  content  of  our  consciousness. 
With  care  we  can  make  it  express  our  intellectual 
judgments,  but  it  fails  lamentably  to  express  our  feel- 
ings and  emotions.     Only  those  who  have  tried  hard 


16  Conclusion 

to  make  others  understand  what  is  going  on  in  their 
minds  can  appreciate  the  insuperable  difficulty  of  the 
task.  It  is  fatally  easy  to  misunderstand ;  all  the  easier 
because  we  do  not  always  wish  to  understand,  or  at  any 
rate  are  not  always  ready  to  take  the  necessary  trouble. 
Language  is  perforce  somewhat  mechanical ;  while 
consciousness  is  living,  warm  and  human.  But  it  must 
not  be  supposed  that  language  is  entirely  mechanical; 
it  lives  in  so  far  as  it  has  power  by  its  associations  to 
revive  past  consciousness.  This  revival  it  is  always 
bringing  about,  but  to  very  different  degrees,  owing  to 
the  different  experiences  of  different  individuals,  their 
different  ways  of  looking  at  things,  their  different 
temperaments,  their  various  powers  of  attention  and 
their  degrees  of  interest. 

Few  people  really  want  to  know  the  truth,  the  whole 
truth,  and  nothing  but  the  truth.  Most  men  want  to 
be  flattered,  to  hear  pleasant  news,  and  to  shut  their 
eyes  to  all  that  is  disagreeable.  It  is  a  human  failing 
to  crave  for  comfort.  It  is  a  fault  with  a  good  side. 
To  fight  on  and  on,  to  hope  against  hope,  never  to 
know  when  one  is  beaten — this  is  a  useful  quality  for 
which  we  should  be  truly  thankful.  But  it  is  a  quahty 
which  is  most  in  place  in  times  of  great  stress  and  in 
critical  moments.  In  the  normal  course  of  everyday 
life  it  is  generally  far  better  to  face  facts  and  to  look 
upon  the  world  honestly  and  frankly.  Deep  down  in 
our  hearts  we  realize  that  truth  may  be  unpleasant  at 
the  moment,  but  that  it  brings  its  reward  afterwards, 
if  not  to  us  at  any  rate  to  our  descendants.  And 
besides  its  utihtarian  value,  truth  is  loved  for  its  own 
sake,  in  spite  of  the  human  selfishness  and  desire  for 
ease  which,  as  I  have  just  said,  so  often  blind  us  to  it. 


Conclusion  17 

Curiosity  is  an  instinct  only  less  powerful  than  the 
craving  for  comfort.  We  want  to  know ;  but  pleasure, 
or  the  fear  of  pain,  bars  the  way.  As  psychologists 
put  it,  the  one  instinct  inhibits  the  other. 

I  have  said  enough  to  show  that  the  habit  of  truth- 
seeking,  no  less  than  that  of  truth-telling,  is  one  which 
needs  cultivation.  We  must  fight  against  sloth,  love 
of  ease,  prejudice,  hostiUty  to  opponents,  greed,  in  fact 
against  all  selfishness  that  may  bhnd  us  to  reaUty.  The 
spirit  of  the  debater,  whose  aim  is,  not  to  discover  truth, 
but  to  score  a  triumph  and  crush  criticism,  is  one  that 
needs  careful  control,  or  even  to  be  entirely  eliminated. 
Reason  must  be  supreme  in  our  fives,  and,  with  one 
important  exception,  refuse  to  acknowledge  any 
superior.  Into  this  exception  I  must  now  go  with 
some  detail. 

Reason  wiU  teU  us  whether  it  is  possible  to  reafize 
our  wishes,  and,  if  so,  how  to  go  to  work  to  realize  them. 
It  will  tell  us  whether  one  wish  clashes  with  another, 
and  how  we  ought  to  arrange  or  systematize  our  wishes 
so  as  to  reaUze  the  highest.  But  beyond  this  it  cannot 
go.  It  cannot  give  us  our  ideal.  That  which  we 
seek  for  its  own  sake  and  not  for  the  sake  of  anything 
else,  that  which  we  value  most  in  our  lives,  is  not  shown 
to  us  by  exercise  of  reason.  How  our  appreciation  of 
an  ideal  comes  to  us  we  cannot,  in  our  present  state  of 
knowledge,  say.  It  grows  and  exists,  and  that  is  all 
we  know.  If  a  man  holds  that  to  be  of  service  to 
humanity  is  the  highest  object  to  which  he  can  devote 
himself,  reasoning  will  not  persuade  him  that  it  is  not, 
any  more  than  it  wiU  persuade  him  that  the  cup  of  tea 
with  one  lump  of  sugar  in  it  is  sweet  if  he  is  not  satisfied 
with  less  than  two. 

J.  2 


18  Conclusion 

In  the  realm  of  ideals,  then,  reason  fails  us.  Else- 
where, however,  it  is  an  aU-powerful  weapon.  This 
being  so,  it  is  our  duty  to  be  on  our  guard  against  the 
imperfections  of  language,  the  instrument  by  which  the 
workings  of  reason  are  communicated  from  man  to  man. 
Snares  of  many  kinds,  as  I  have  already  said,  he  all 
about  us.  It  is  so  easy  to  misunderstand,  so  difficult 
to  make  oneself  understood.  Rhetoric  may  dazzle  us ; 
cleverness  may  deceive  us ;  our  attention  may  be  caught 
by  one  statement  so  that  everything  else  is  utterly 
neglected.  Against  these  and  similar  dangers  there  are 
no  safeguards  except  love  of  truth  and  constant  prac- 
tice in  seeking  it  and  in  expressing  it  to  others. 


CHAPTER   III 

Scientific  Method. 

Suppose  you  have  before  you  a  basket  of  apples, 
and  you  wish  to  discover  which  are  best  to  eat.  What 
you  say  to  yourself  is  this.  "The  green  apples  are  not 
ripe,  but  the  yellow  and  red  ones  can  do  me  no  harm." 
This  reasoning  is  really  a  compressed  argument,  or 
rather  a  compression  of  two  arguments,  which,  when 
fully  expressed,  would  run  thus : — 

Green  apples  are  not  ripe,  but  red  and  yellow  are. 

These  are  green,  those  are  red  and  yellow. 

Therefore  these  are  not  ripe,  those  are. 

Ripe  apples  are  good  to  eat,  unripe  are  not. 

Those  apples  are  ripe. 

Therefore  those  apples  are  good  to  eat. 
This  kind  of  reasoning,  in  which  a  particular  case  is 
brought  under  a  general  rule,  is  called  deduction.  But 
let  us  suppose  that  you  did  not  know  the  general  rule 
that  unripe  or  green  apples  are  not  good  to  eat.  How 
would  you  go  to  work?  It  would  be  necessary  to  go 
through  a  long  series  of  experiments.  You  would  have 
to  try  each  apple,  and  notice  (1)  its  effects  when  eaten 
and  (2)  its  appearance,  taste  and  so  forth.  The  next 
step  would  be  to  try  to  connect  (1)  and  (2).     You  would 

2—2 


20  Scientific  Method 

probably  conclude  that  green  apples  cause  pain  while 
yellow  and  red  ones  do  not.  Such  a  generalization  is 
roughly  true,  but  is  not,  as  you  probably  know,  quite 
accurate ;  some  greenish  apples  are  not  at  all  bad  to  eat. 
The  generaUzation  can  be  improved  only  by  further 
experiment,  and  the  greater  the  number  of  experiments 
the  more  exact  the  hypothesis,  as  it  is  called,  can  be 
made.  Some  hj^otheses  sum  up  the  experience  of  the 
human  race  during  hundreds  of  years.  This  second 
kind  of  reasoning,  the  framing  of  generahzations,  is 
called  induction. 

Both  kinds  of  reasoning  are  valuable,  but  it  is  the 
second  kind  which  increases  our  knowledge  and  enables 
us  to  acquire  greater  control  over  nature ;  the  former 
kind  is  chiefly  useful  in  enabling  us  correctly  to  make 
use  of  knowledge  already  acquired.  Therefore  we  will 
discuss  induction  before  deduction. 

Induction. 

Every  vaUd  induction  consists  of  at  least  three 
stages : — 

(1)  The  collection  of  facts. 

(2)  The  framing  of  the  hj^othesis. 

(3)  The  testing  of  the  hypothesis. 

The  facts  may  have  to  be  arranged  or  classified  as 
well  as  collected,  and  the  testing  of  the  hypothesis 
may  result  in  a  modification  of  it,  or  even  in  its  entire 
abandonment.  Let  us  take  a  simple  instance  of 
induction,  and  paj^  due  attention  to  the  three  stages 
given  above. 

Problem.     In  what  conditions  does  a  candle  burn? 

Collection  of  facts.     We  notice  first  of  all  that  in  air 


huluction  21 

a  candle  will  not  burn  unless  it  is  heated  to  a  certain 
temperature.  We  assume  then  that  heat  is  a  necessary 
condition  if  the  candle  is  to  burn.  It  is  now  possible, 
though  perhaps  not  wise,  to  frame  a  hypothesis. 

Hypothesis.  A  candle  burns  if  heated  to  a  certain 
temperature. 

Test.  If  a  certain  degree  of  heat  is  sufficient  to 
make  a  candle  burn,  it  wdll  burn  if  heated  to  that  degree 
in  carbon  dioxide.  Accordingly  we  proceed  to  do  this, 
and  find  that  the  candle  does  not  burn.  Our  hypothesis 
then  was  inaccurate.  Besides  heat,  a  certain  kind,  or 
certain  kinds,  of  air  are  necessary.  We  know  that  the 
candle  burns  in  atmospheric  air,  so  we  now  try  whether 
it  burns  in  the  separate  components  of  air.  Experi- 
ments will  show  us  that  in  nitrogen,  one  of  the  compo- 
nents of  air,  the  candle  never  burns.  In  the  other 
component,  oxygen,  it  burns  readily.  We  therefore 
modify  our  first  hypothesis. 

Emended  hypothesis.  A  candle  burns  if  heated  to 
a  certain  temperature  in  oxygen. 

Repeated  experiments  always  confirm  the  truth  of 
this  hypothesis.  But  if  we  consider  our  problem  once 
more  we  shall  see  that  we  have  given  only  a  partial 
solution  of  it.  For  all  we  know  there  may  be  other 
gases  or  mixtures  of  gases  in  which  a  candle  will  burn, 
and  in  some  cases  perhaps  even  heat  will  not  be  neces- 
sary. Only  repeated  experiment  can  tell  us  whether 
these  possibilities  correspond  to  reahty  or  not. 

The  example  just  given  well  illustrates  the  danger 
of  hasty,  and  therefore  imperfect,  generahzation. 
Haste,  in  fact,  is  the  cause  of  most  of  the  mistakes  made 
in  scientific  inquiry.  Whenever  the  evidence  is  not 
sufficient,  the  only  scientific  thing  to  do  is  to  refrain 


22  Induction 

from  framing  a  hypothesis  until  more  evidence  is 
obtained.  Strictly  speaking,  we  ought  to  collect  every 
shred  of  available  evidence  before  generahzing,  but  to 
this  rule  there  is  an  important  exception.  This  excep- 
tion is  really  a  concession  to  the  weakness  and  imper- 
fection of  the  human  mind.  To  collect  all  the  evidence 
is  sometimes  too  laborious  a  task ;  so  a  representative 
part  is  taken  and  a  working  hypothesis,  as  it  is  called, 
formed  from  it.  This  working  or  tentative  hypothesis 
is  only  provisional,  and  it  must  be  continually  tested 
by  comparison  with  reaUty  as  new  evidence  presents 
itself.  Should  facts  be  discovered  which  will  not  fit  in 
with  the  hypothesis  it  must  be  modified  or  abandoned 
at  once.  Truth  must  never  be  ignored  or  distorted  in 
order  to  save  a  hypothesis.  The  human  mind  is  often 
tempted  to  be  dishonest  in  this  way,  because  it  is 
natural  that  a  hypothesis  should  be  loved  by  its  author ; 
it  has  been  said  that  the  "saddest  sight  in  the  world  is 
a  theory  slain  by  a  fact."  I  will  now  show  the  useful- 
ness of  a  working  hypothesis  by  considering  what  the 
factors  are  that  determine  the  position  of  large  cities. 
To  solve  this  problem  fully  it  would  be  necessary 
to  examine  the  sites  of  every  large  town  that  exists  or 
has  existed,  and  to  inquire  into  the  history  of  the  founda- 
tion of  each  one.  But  a  great  deal  of  this  evidence 
has  perished,  while  to  collect  and  examine  all  that  does 
exist  is  a  very  long  and  laborious  work ;  indeed  it  could 
not  be  done  at  all  were  it  not  for  the  patience  and 
diUgence  of  numberless  geographers  and  historians, 
living  and  dead.  Unless,  therefore,  we  are  prepared  to 
devote  months  or  even  years  of  unremitting  toil  to  the 
solution  of  this  problem  we  must  be  content  with  a 
working  hypothesis  derived  from  such  evidence  as  is 


Induction  23 

of  easy  access,  and,  aware  of  its  tentative  nature,  be 
ready  to  modify  or  abandon  it  at  any  moment.  We 
might  open  a  gazetteer  at  random  and  choose  any 
twenty-five  towns  with  over  30,000  inhabitants.  An 
examination  of  the  sites,  combined  with  the  study 
of  history,  would  probably  show  that  the  main  reasons 
for  the  rise  of  these  towns  are : — 

(1)  Nearness  to  a  trade  route. 

(2)  Situation  in  a  region  of  great  natural  fertiHty. 

This  classification  of  the  evidence  leads  to  the  forma- 
tion of  a  provisional  hypothesis,  which  subsequent 
experience  will  modify,  probably  by  the  addition  of 
other  reasons  for  the  choice  of  sites. 

It  must  not  be  thought  that  the  mere  application 
of  certain  rules  will  lead  to  important  discoveries. 
Scientific  method  is  not  a  machine ;  it  will  not  work 
by  itself,  but  needs  the  co-operation  of  human  qualities. 
Care,  thoroughness  and  observation  are  required  for 
the  collection  of  evidence ;  insight  and  imagination 
are  essential  for  a  good  hypothesis ;  acuteness  must  be 
exercised  in  applying  tests.  Some  important  discoveries 
appear  to  have  been  little  more  than  brilUant  guesses ; 
so  rapid,  so  intuitive  was  the  working  of  the  scientist's 
brain.  Drill  and  routine,  however,  are  by  no  means 
to  be  despised.  They  are  useful  even  to  the  genius; 
while  to  the  rank  and  file  they  are  invaluable,  and  it 
must  be  remembered  that  to  the  laborious  spade-work 
of  obscure  persons  is  due  many  a  clever  hypothesis 
framed  by  a  greater  mind. 

When  we  test  a  hj'pothesis,  sometimes  we  look  out 
for  fresh  evidence,  and  sometimes  we  conduct  an  experi- 
ment. The  essence  of  an  experiment  is  to  allow  natural 
forces  to  work  when  under  the  control  of  the  observer. 


24  Induction 

Suppose,  for  instance,  it  is  observed  that  wheat  grows 
well  in  certain  districts,  and  we  wish  to  know  which 
quality,  or  which  quaUties,  of  these  districts  produce 
the  good  results.  Possibly  we  may  frame  the  hypo- 
thesis, after  due  consideration  of  all  the  districts,  that 
their  fertility  is  caused  by  the  amount  of  water  at  a 
certain  depth  below  the  surface  of  the  soil.  If  by 
drainage  we  can  vary  this  amount  of  water  and  then 
grow  a  crop,  we  have  a  very  good  test  of  our  hypothesis. 
Should  the  crop  be  as  good  as  before,  the  hypothesis 
was  wrong;  should  it  be  inferior,  the  water  was  one 
cause,  and  perhaps  the  only  cause,  of  the  fertility. 
Whether  other  causes  were  operating  can  be  decided 
only  by  varying  the  other  conditions  one  at  a  time.  If 
more  than  one  condition  be  varied  at  one  and  the  same 
time,  it  is  impossible  to  decide  whether  any  resulting 
change  is  caused  by  one  factor  only  or  by  more  than 
one. 

Before  going  on  to  discuss  the  nature  of  evidence 
it  will  be  wise  to  recapitulate  what  I  have  already  said 
about  hypotheses.  It  is  such  an  important  question 
that  a  httle  repetition  can  do  no  harm. 

Recapitulation. 

A  hypothesis  is  a  statement  of  a  unity  assumed  to 
underhe  a  number  of  facts.  In  other  words  it  is  an 
attempt  to  explain  phenomena  by  pointing  out  how 
they  are  related.  If  you  see  a  doctor's  carriage  outside 
the  house  of  a  friend  who  is  often  ill,  it  is  a  hypothesis 
to  suppose  that  the  doctor  has  been  called  in  to  attend 
your  friend.  This  is  an  eminently  reasonable  but  not 
necessarily   a   correct   hypothesis.     The   carriage  may 


Recapitulation  25 

be  where  it  is  by  accident,  or  the  doctor  may  be  attend- 
ing another  inmate  of  your  friend's  house.  A  traveller 
might  perhaps  sum  up  his  experience  in  the  hypothesis 
that  all  good  hotels  are  expensive.  This  hypothesis, 
again,  is  Ukely  to  be  true,  but  the  discovery  of  a  good, 
cheap  hotel  would  necessitate  a  modification  of  it. 

The  most  valuable  hypotheses  are  those  which  state 
a  general  rule  summing  up  a  number  of  particular  in- 
stances. These  make  progress  possible  by  putting 
information  in  a  handy  form.  These  hypotheses,  when 
well  verified,  themselves  become  data  for  yet  wider 
generalizations,  and  this  process  is  ever  going  on  under 
the  guidance  of  our  scientific  workers  and  thinkers. 
In  this  way  our  knowledge  is  becoming  more  and  more 
ordered  and  organized  as  well  as  wider  and  deeper. 

Some  hypotheses  can  be  conclusively  proved  or  dis- 
proved by  a  little  inquiry.  It  would  not  take  long,  for 
instance,  to  find  out  whether  in  the  example  given 
above  the  doctor  was  or  was  not  visiting  your  sick 
friend.  But  in  other  cases  complete  verification  is 
absolutely  or  at  any  rate  practically  impossible,  how- 
ever highly  probable  the  hypothesis  can  be  shown  to  be. 
That  all  diamonds  will  cut  glass  is  a  hypothesis  which 
has  been  confirmed  millions  of  times ;  you  may  be  confi- 
dent that  any  particular  diamond  will  have  this  power. 
Yet  at  any  time,  however  unlikely  the  supposition,  a 
diamond  may  be  found  too  soft  to  cut  glass. 

If  two  volumes  of  hydrogen  and  one  of  oxygen  be 
mixed  and  then  exploded,  the  result  is  that  all  the 
hydrogen  and  oxygen  disappear,  and  a  little  water  is 
formed.  The  experiment  has  been  performed  a  count- 
less number  of  times  and  the  result  is  always  the 
same. 


26  Recapitulation 

Scientists  are  thus  enabled  greatly  to  shorten  their 
work.  One  experiment  carefully  performed  is  often 
sufficient  to  prove  a  new  generahzation.  Hj^potheses, 
however,  which  are  based  on  one  experiment  are  often 
wrong,  because  it  is  difficult  to  make  quite  sure  that  all 
the  conditions  have  been  taken  into  account.  Without 
our  knowing  it,  an  essential  condition  in  a  first  experi- 
ment may  have  been  a  temperature  of  no  more  than 
70°  C.  In  a  second  experiment  the  result  will  not  be 
the  same  if  by  accident  the  temperature  is  raised  to 
73°  C. 

Evidence. 

By  evidence  we  mean  accurately  observed  phenomena 
of  all  kinds  which  seem  to  be  causally  connected.  Other 
words  used  to  denote  the  same  thing  are  data,  facts  and 
nmterial.  The  collection  of  facts  is  usually  a  long  and 
laborious  process,  but  obviously  no  advance  in  science 
is  possible  without  it.  It  will  be  useful  to  examine  the 
nature  of  evidence  by  taking  a  very  common  type  of 
problem.  We  are  constantly  applying  scientific  method 
in  our  everyday  life ;  there  is  only  one  way  to  discover 
truth,  whether  that  truth  be  important  or  trifling. 
Suppose  a  short-sighted  person  were  going  along  a 
country  road  and  observed  a  black  object  moving 
towards  him  in  the  distance.  He  might  argue  in  the 
following  way: — 

"Since  the  object  is  moving  steadily  it  must  be 
either  alive  or  mechanically  propelled.  No  motor  or 
bicycle  would  use  this  bad  road  when  there  is  a  good 
road  a  few  hundred  yards  to  the  right  leading  to  the 
same  destination.  It  may  be  a  black  animal,  but  no 
animal  that  I  know  of  is  of  the  shape  and  size  it  appears 


Evidence  27 

to  have.  It  looks  like  a  man,  and  I  was  told  in  the  last 
village  that  the  postman  passes  along  this  road  at  about 
this  time.  Now  that  I  come  to  think  of  it,  the  pace 
is  too  slow  even  for  a  bicycle,  and  I  think  that  I  can  see 
a  postman's  pack.  I  conclude  that  it  is  the  postman 
and  that  he  is  dressed  in  very  dark  clothes.  If  I  wait 
until  my  short  sight  has  a  better  opportunity  I  shall  be 
able  to  test  my  conclusion." 

The  evidence  used  by  this  person  can  be  classed 
under  three  main  heads: — 

(1)  Sense-impressions,  i.e.  the  shape,  size,  colour 
and  movement  of  the  object. 

(2)  Past  personal  experience,  i.e.  the  size  and 
shape  of  various  animals  and  of  men,  the  speed  of  motors 
and  of  bicycles,  and  the  improbabihty  of  meeting  these 
on  bad  roads. 

(3)  The  testimony  of  other  people,  i.e.  the  infor- 
mation about  the  postman. 

My  analysis  is  not  quite  complete,  but  it  is  accurate 
enough  to  illustrate  the  points  I  wish  to  make  clear. 
The  first  is  that  both  (2)  and  (3)  consist  of  generaliza- 
tions, which  have  been  reached  as  the  result  of  many 
past  experiences.  Such  generalizations  are  often  of 
value  as  furnishing  material  for  yet  wider  generahza- 
tions  or  (as  here)  because  they  can  be  applied  as  tests 
to  tentative  hypotheses.  What  really  has  taken  place 
in  the  mind  of  the  short-sighted  person  is  as  foUows. 
He  has  observed  a  moving,  black  shape.  He  then 
proceeds  to  make  a  series  of  hypotheses,  which  he  tests 
one  by  one.  Each  test  is  a  deduction  from  a  well- 
estabhshed  generah'zation.  One  example  will  make 
the  process  plain. 

Hypothesis.     This  object  may  be  a  motor. 


28  Evidence 

Test.  If  it  is  a  motor,  like  all  motors  it  will  keep  if 
possible  to  good  roads.  But  the  road  on  which  it  is 
is  a  bad  one,  although  a  good  one  is  available.  There- 
fore the  object  is  not  a  motor. 

The  third  kind  of  evidence  is  a  statement  (in  this 
case  a  general  one)  accepted  on  the  authority  of  others. 
This  sort  of  evidence  is  very  important,  and  great  care 
must  be  taken  to  measure  correctly  its  credibihty.  The 
science  of  history  depends  largely  upon  the  testimony 
of  others. 

Bearing  in  mind  this  analysis  let  us  consider  another 
simple  problem.  A  medical  officer  is  summoned  to 
investigate  an  epidemic  of  scarlet  fever  in  a  small  town 
of  20,000  inhabitants.  His  object  is  to  discover  the 
cause  of  the  outbreak,  in  order  if  possible  to  remove  it. 
He  first  has  a  list  made  of  all  the  cases,  with  the 
addresses  of  the  patients  and  the  dates  of  their  coming 
under  medical  supervision.  There  are  in  all  530  cases. 
These  are  not  confined  to  one  quarter  of  the  town,  but 
certain  streets  suffer  very  severely,  although  widely 
separated,  while  other  streets  close  to  one  another 
scarcely  suffer  at  all.  Houses  seem  to  be  attacked 
rather  than  single  individuals.  There  are  many  houses 
in  which  nearly  every  inmate,  with  the  exception  of 
those  immune  through  having  had  the  disease  before, 
has  fallen  a  victim.  A  week  before  there  were  no 
cases  at  all  in  the  town;  for  the  last  four  days  they 
have  been  occurring  at  the  rate  of  over  100  a  day. 

Such  is  the  evidence  before  the  medical  officer.  It 
should  be  noticed  that,  whereas  in  the  last  problem 
certain  simple  sense-impressions  required  interpretation, 
it  is  now  a  question  of  interpreting  again  a  number  of 
interpreted    sense-impressions.     Moreover,    the    officer 


Evidence  29 

takes  most  of  the  evidence  on  trust,  accepting  as  true 
the  statements  of  his  co-workers.  If  these  are  both 
capable  and  trustworthy  he  is  quite  justified  in  so 
doing,  but  if  he  doubts  either  the  capacity  or  the 
honesty  of  any  one  of  these  it  is  his  duty  to  verify  all 
testimony  received  from  him.  We  will  assume,  how- 
ever, that  such  verification  is  not  necessary. 

The  officer  now  proceeds  to  frame  a  tentative  or 
working  hypothesis.  Is  it  an  instance  of  simple  infec- 
tion from  patient  to  patient?  This  hypothesis  is  at 
once  rejected  because  of  the  ofiicer's  past  experience 
and  the  knowledge  he  has  gained  from  the  experi- 
ence of  other  observers.  It  does  not  account  for  the 
suddenness  of  the  outbreak,  nor  yet  for  the  simultaneous 
seizure  of  whole  famihes.  An  epidemic  caused  by 
repeated  contact  would  be  gradual,  and  would  probably 
spread  from  district  to  district  surely  but  slowly.  The 
swift  onslaught  of  the  epidemic  under  consideration 
points  to  a  cause  affecting  large  numbers  of  people  at 
one  and  the  same  time.  So  the  officer  frames  another 
hjrpothesis.  He  has  heard  that  at  a  village  five  miles 
away  scarlet  fever  has  occurred  several  times  during 
the  last  few  months.  Once  more  the  evidence  is  but 
testimony  depending  upon  the  authority  of  others, 
but  there  seems  to  be  no  reason  to  distrust  it.  This 
village  sends  milk  to  one  of  the  chief  milk  distributers 
of  the  town.  Accordingly  the  new  hypothesis  is  that 
the  epidemic  is  due  to  contaminated  milk.  The  officer 
knows  that  outbreaks  are  often  caused  in  this  way. 
This  hypothesis  is  tested  by  a  deduction  which  will 
correspond  to  facts  if  the  hypothesis  be  correct.  If 
milk  be  the  cause  of  the  outbreak,  the  "fever  map" 
will  correspond   to   the   "round"   of  some   milkman. 


30  Evidence 

Investigation  shows  that  the  infected  houses  are  in 
every  case  supphed  by  the  milkman  who  gets  his  milk 
from  the  infected  village.  The  hypothesis  is  now 
almost  certainly  correct,  but  in  order  to  be  quite  sure 
of  his  ground  the  officer  makes  inquiries  at  the  suspected 
village,  and  finds  one  of  the  chief  milkers  suffering  from 
scarlet  fever  in  its  most  infectious  stage.  This  man 
is  isolated,  the  supply  of  milk  from  the  village  is  sus- 
pended and  the  epidemic  rapidly  declines. 

These  instances  show  very  well  that  evidence  does 
not  always  consist  of  uninterpreted  sense-impressions. 
Data  are  often  the  results  of  a  whole  series  of  inferences 
and  interpretations,  which  in  very  many  cases  depend 
upon  the  capacity  and  honesty  of  numerous  observers. 
It  may  be  said,  I  think,  that  the  careful  investigator 
will  always  bear  in  mind  the  necessity  of  reahzing 
which  kind  of  evidence  he  is  using  and  the  ways  in 
which  error  may  creep  into  each.  Sense-impressions 
may  be  misinterpreted ;  generahzations  may  be  faulty ; 
witnesses  may  be  incompetent  or  dishonest. 

Of  all  evidence  that  which  rests  upon  the  authority 
of  others  is  the  most  liable  to  error.  Few  men  are 
perfectly  honest;  we  are  all  occasionally  guilty  of 
allowing  our  intellect  to  be  perverted  by  our  emotions. 
No  man  can  be  a  just  judge  of  an  adversary.  Then 
again,  however  honest  we  may  be,  we  may  make  intel- 
lectual mistakes  through  lack  of  power  or  through 
carelessness.  Finally,  whether  these  dangers  are  over- 
come or  not,  we  may  express  our  conclusions  in  faulty 
language  conveying  to  others  a  series  of  wrong  impres- 
sions. It  is  not  wonderful  that  testimony  depending 
upon  the  authority  of  others  always  stands  in  need  of 
the  closest  scrutiny  before  it  can  be  accepted. 


it 


Evide7ice  31 

We  must  now  consider  some  of  the  tests  that  can 
be  applied  to  the  testimony  of  others  in  order  to  estimate 
its  credibiUty.  We  can  bring  forward  evidence  of  two 
kinds : — 

(1)  intrinsic; 

(2)  extrinsic. 

By  "intrinsic"  evidence  is  meant  a  consideration 
of  the  inherent  probabihty  that  an  alleged  occurrence 
took  place.  If  a  statement  be  in  accordance  with 
normal  experience  it  is  more  likely  to  be  true  than  if 
it  is  opposed  to  it.  But  even  if  the  statement  be  in 
itself  hkely,  its  credibility  is  doubtful  if  its  author 
be  known  to  be  inaccurate,  habitually  untruthful,  or 
likely  to  profit  by  telUng  a  falsehood.  By  "extrinsic" 
evidence  is  meant  a  consideration  of  the  statements  of 
other  witnesses  or  of  well-ascertained  facts.  If  extrinsic 
evidence  be  perfectly  reliable,  it  may  convict  a  state- 
ment of  untruth,  or,  on  the  other  hand,  it  may  strongly 
confirm  it.  A  very  common  occurrence  is  that  two 
statements,  made  by  two  different  authorities  of  nearly 
equal  credibihty,  contradict  each  other.  To  decide 
which  of  the  two  statements  is  true  is  then  a  matter  of 
the  greatest  difficulty.  Sometimes  it  so  happens  that 
a  piece  of  extrinsic  evidence  presents  itself  which  is  of 
such  a  kind  that  one  or  other  of  the  statements  is 
strongly  confirmed  if  not  proved,  but  sometimes  we 
have  to  be  content  with  an  uncertainty  of  the  vaguest 
kind.  The  science  of  history  is  almost  entirely  depend- 
ent upon  evidence  the  truth  of  which  cannot  be  proved. 
But  usually  there  is  no  reason  to  doubt  the  general 
accuracy  of  our  authorities;  when  two  clash  it  is  in 
most  cases  possible  to  say  that  one  or  the  other  is  more 
likely  to  be  true ;  in  a  few  cases,  however,  the  evidence 


32  Evidence 

on  either  side  is  evenly  balanced,  and  it  is  quite  impos- 
sible to  decide  which  is  the  more  likely  view  to  hold. 

Decision  between  conflicting  testimony  is  the  task 
which  faces  our  judges  and  jurymen  when  they  are 
trjdng  a  case.  The  lawyers  of  both  parties  do  their 
utmost  to  put  their  side  of  the  question  in  the  best 
possible  hght,  and  there  is  httle  chance  of  any  pertinent 
evidence  or  plausible  interpretation  being  overlooked. 
Perhaps  a  greater  danger  is  that  a  brilhant  advocate, 
by  clever  rhetoric  or  by  the  magnetism  of  his  personahty, 
may  bUnd  the  jurymen  to  the  conclusion  to  which  the 
evidence  really  points ;  the  judge,  however,  is  specially 
trained  to  detect  such  disturbing  influences,  and 
puts  the  jurymen  on  their  guard  when  he  addresses 
them. 

Every  day  of  our  Hves  we  are  occupied  with  the 
same  task  of  solving  Uttle  problems  in  which  we  have 
to  decide  between  conflicting  evidence.  Suppose  for 
instance  that  we  are  marketing  and  wish  to  buy  some 
fish.  We  go  to  a  fishmonger  and  ask  for  some  plaice. 
He  gives  us  the  quantity  asked  for  and  assures  us  that 
it  is  fresh.  But  when  we  see  it  we  have  our  suspicions 
of  its  quaHty,  and  friends  have  warned  us  that  this 
particular  dealer  is  not  always  to  be  trusted.  How  are 
we  to  decide  whether  we  ought  to  buy  the  fish  or  not  ? 
Are  we  to  believe  the  fishmonger  or  our  owti  suspicions  ? 
Now  the  former  has  a  reputation  for  deceit,  and  the 
hypothesis  that  the  fish  is  not  fresh  fits  in  better  with 
the  data  before  us.  Therefore,  if  we  are  wise,  we  shall 
refuse  to  buy  the  fish. 

Problems  such  as  this  constantly  present  themselves 
for  solution  in  the  lives  of  all  of  us.  We  are  so  used  to 
them  that  we  are  rarely  conscious  of  going  through  the 


Classijicatiou  33 

stages  of  a  formal  proof.     Our  mind  works  rapidly  and 
as  it  were  by  intuition. 

In  collecting  evidence  and  in  examining  it  accuracy 
is  essential.  Accurate  measurement  is  the  basis  of  all 
science.  Not  only  accurate  reasoning  but  also  accurate 
senses  are  necessary.  To  be  able  to  make  a  line  of 
exactly  a  given  length,  to  distinguish  slight  differences 
of  colour,  smell  or  taste,  to  notice  minute  changes,  all 
these  powers  are  at  least  as  important  in  scientific  work 
as  logical  acuteness.  Many  an  experiment  has  been  an 
utter  failure  just  because  some  slight  error  has  occurred 
in  measurement,  and  many  a  discovery  has  been  missed 
through  failure  to  observe  a  shght  change  in  the  course 
of  an  experiment. 

Classification. 

In  many  cases  we  find  that  the  evidence  after  being 
collected  needs  arranging.  Suppose  for  example  that 
we  are  considering  the  resemblance  of  certain  animals 
to  their  environment.  When  all  the  facts  have  been 
collected  it  is  found  that  they  naturally  fall  into  two 
groups:  (1)  cases  in  which  the  resemblance  enables  an 
animal  to  escape  from  an  enemy;  (2)  cases  in  which 
the  resemblance  enables  an  animal  to  capture  its  prey. 
This  classification  greatly  facilitates  the  framing  of  a 
hypothesis. 

We  classify  things  and  arrange  them  into  groups 
because  of  likenesses  and  unlikenesses.  We  put  into 
one  group  all  things  that  are  brown,  into  another  all 
things  that  are  green,  and  so  on.  Again,  we  can 
arrange  things  according  to  size  or  shape,  and  persons 
according  to  their  physical  or  mental  characteristics. 

J.  3 


34  Classification 

But  when  we  are  classifying  for  scientific  purposes  we 
must  be  careful  not  to  be  misled  by  resemblances 
which  do  not  affect  our  problem.  Only  those  count 
which  are  actually  related  to  the  special  point  that 
we  are  considering.  If  we  have  to  classify  books  for 
a  hbrary  we  gain  nothing  by  dividing  them  into  groups 
based  upon  the  colour  or  the  material  of  their  binding. 
An  index  of  bindings  would  be  of  no  use  to  a  student 
consulting  the  library.  We  shall  probably  base  our 
classification  upon  the  subject-matter  of  the  books 
and  place  all  the  history  books  in  one  group,  all  the 
novels  into  another  group,  and  so  on.  An  index  of 
authors  is  also  very  useful,  and  the  various  subjects 
might  be  re-classified  upon  this  basis.  The  most 
important  thing  to  avoid  in  classification  is  what  is 
known  as  cross  division,  in  other  words  our  groups 
must  be  mutually  exclusive.  It  would  never  do  to 
divide  men  into  (1)  good  men,  (2)  Frenchmen,  (3)  one- 
legged  men,  (4)  dark  men,  (5)  clever  men,  and  (6)  old 
men.  This  example  is  obviously  absurd;  the  groups 
are  not  mutually  exclusive,  and  the  classification,  if 
such  it  can  be  called,  serves  no  useful  purpose  what- 
soever. 

Knowledge  itself  has  often  been  divided  into  groups, 
but  a  classification  of  the  sciences  can  never  be  really 
satisfactory.  The  universe  is  a  unity,  and  science, 
that  is  man's  comprehension  of  the  universe,  must 
be  a  unity  also.  All  attempts  to  divide  this  unity 
necessarily  fail.  Nevertheless  even  an  imperfect  classi- 
fication of  the  sciences  is  useful  for  practical  purposes, 
and  an  attempt  to  classify  them  will  at  any  rate 
demonstrate  how  intimately  connected  they  aU  are. 

First  there  is  a  group  of  sciences  which  deal  with 


Classification  35 

the  properties  of  matter,  whether  animate  or  inanimate, 
and  with  the  forces  which  manifest  themselves  in 
conjunction  with  matter;  e.g.,  chemistry  and  heat. 

There  is  another  group  that  deals  with  the  pheno- 
mena peculiar  to  living  bodies ;  e.g.,  physiology  and 
botany. 

There  is  another  group  dealing  with  animals,  and 
in  particular  with  man,  in  so  far  as  they  are  conscious 
beings  with  instincts,  impulses,  desires  and  reasoning 
powers.  In  this  group  are  included  ethics,  psychology 
and  logic. 

The  mathematical  sciences  deal  with  the  properties 
of  number  and  space. 

Each  of  these  groups  is  subdivided,  and  there  are 
certain  sciences  which  belong  to  more  than  one  group. 
Geography,  for  instance,  has  affinities  with  geology, 
which  is  one  of  the  physical  sciences,  and  with  sociology, 
which  belongs  to  the  same  group  as  ethics.  Where 
ought  history  to  be  placed  ?  Being  the  story  of  human 
development  it  is  akin  to  sociology,  but  geographical 
factors  have  exerted  such  a  powerful  influence  upon 
man  that  its  relationship  to  geography  cannot  be  denied. 
The  science  of  language  is  another  one  which  is  very 
difficult  to  place  in  a  definite  class.  We  are  learning 
more  and  more  every  day  how  strong  is  the  influence 
of  physiological  factors  upon  the  history  of  language, 
but  it  is  the  laws  of  mental  life  that  determine  most 
linguistic  phenomena. 

The  various  sciences,  in  fact,  shade  into  one  another. 
Forms  of  energy  are  constantly  changing  without  the 
amount  of  energy  becoming  either  greater  or  less. 
Heat  passes  into  electricity  and  electricity  causes 
chemical  action;    motion  is  exchanged  for  heat  and 

3—2 


36  Classification 

heat  for  motion.  No  definite  line  can  be  drawn  between 
one  natural  class  and  its  near  neighbours;  Darwin's 
great  work  was  to  show  how  species  gradually  give 
rise  to  other  species.  Similarly  the  sciences  are  not 
separated  by  hard  and  fast  boundaries.  Nevertheless, 
in  spite  of  the  absence  of  fixed  limits,  there  is  a  differ- 
ence between  one  natural  class  and  another  and 
between  one  science  and  another.  We  may  not  be 
sure  where  heat  begins  and  chemistry  ends,  but  we 
are  quite  certain  that  when  iron  rusts  it  is  a  phenomenon 
of  chemistry  and  not  of  heat. 

As  our  knowledge  grows  we  reahze  more  clearly 
the  unity  underlj^dng  it.  At  the  same  time  the  sciences 
tend  to  increase  in  number  through  subdivision.  A 
few  years  ago  a  great  French  scholar,  by  carefully 
investigating  the  changes  that  take  place  in  the  mean- 
ings of  words  as  time  goes  on,  founded  the  science  of 
semantics,  a  subdivision  of  the  science  of  language. 
Other  new  sciences  are  eugenics,  a  branch  of  biology, 
deahng  with  the  laws  according  to  which  characteristics 
are  transmitted  from  parent  to  offspring,  and  bio- 
chemistry, a  branch  of  chemistry  deahng  with  the 
chemical  changes  that  take  place  in  Hving  bodies. 

Notable  Examples  of  Scientific  Discoveries. 

(1)  One  of  the  most  interesting  examples  of  scien- 
tific induction  is  to  be  found  in  the  history  of  malaria. 
Malaria  is  a  fever  which  from  the  very  earUest  times 
has  afflicted  dweUers  in  the  neighbourhood  of  marshes. 
Very  naturally  the  ancients  concluded  that  the  disease 
was  caused  by  the  water,  or  by  exhalations  from  it. 
This  view  was  held  until  quite  modern  times,  and  as 


Notable  Examples  of  Scientific  Discoveries     37 

to  avoid  marshes  was  followed  by  excellent  results, 
there  did  not  seem  to  be  any  reason  to  abandon  the 
theory.  But  modem  science  was  not  satisfied.  Why 
are  some  marshes  unhealthy  and  not  others?  Why 
should  autumn  be  the  most  unhealthy  season  of 
the  year?  These  and  many  other  considerations  of 
a  like  nature  caused  scientists  to  search  for  another 
hjrpothesis.  A  famous  doctor,  Sir  Patrick  Manson, 
argued  that  malaria  might  be  caused  not  by  marshes 
but  by  something  that  can  only  be  found  near  marshes. 
So  he  suggested  that  the  disease  was  caused  by  the 
bite  of  a  mosquito.  This  suggestion  was  httle  more 
than  a  guess.  But  it  attracted  the  attention  of  a 
doctor  of  the  Indian  Army,  who  is  now  Sir  Ronald 
Ross.  Several  years  before  it  had  been  proved  that 
in  the  blood  of  malaria  patients  there  could  always 
be  found  by  the  aid  of  the  microscope  certain  parasites 
in  one  stage  (the  asexual)  of  their  development.  This 
process  of  reproduction  cannot  go  on  indefinitely;  a 
sexual  stage  must  occur  somewhere,  and  there  were 
several  strong  reasons  for  supposing  that  it  took  place 
outside  the  human  being.  The  question  before  Ross 
was  this.  Could  he  find  signs  of  this  sexual  stage  in 
the  blood  of  mosquitoes?  For  over  two  and  a  half 
years  he  worked  incessantly,  examining  under  the 
microscope  many  thousands  of  insects  without  the 
slightest  sign  of  the  object  of  his  search.  Practically 
all  this  work  was  done  on  one  species  of  mosquito, 
which  happened  to  be  the  most  common  kind  in  that 
region  of  India  in  which  Ross  was  working.  Almost  in 
despair,  he  chanced  to  receive  from  a  friend  a  different 
mosquito,  and  in  the  walls  of  its  stomach  he  found 
the  black  pigment  which  is  deposited  within  the  body 


38  Notable  Examples  of 

of  the  malaria  parasite  as  it  feeds  and  grows.  Further 
investigation  showed  that  this  substance  could  always 
be  found  in  the  walls  of  the  stomach  of  this  species  of 
mosquito  a  few  days  after  it  had  bitten  a  malaria 
patient.  This  discovery  was  made  in  the  year  1898. 
Two  more  years  of  study  and  experimentation  unfolded 
the  whole  life-history  of  the  parasite,  both  its  asexual 
stage  in  man  and  its  sexual  stage  in  the  mosquito. 
Only  the  AnopheUne  group,  it  was  shown,  could  carry 
malaria  from  man  to  man. 

In  1900  two  EngHsh  doctors  lived  in  the  Roman 
Campagna,  a  district  infested  with  malaria,  for  the 
worst  months  of  the  j^ear.  They  exposed  themselves 
freely  to  all  kinds  of  weather,  and  did  everything 
popularly  supposed  to  cause  malaria,  but  they  pro- 
tected themselves  with  the  greatest  care  against 
mosquito  bites.  They  took  no  quinine,  the  recognized 
specific  for  malaria.  Although  all  their  neighbours 
had  malaria,  they  themselves  were  entirely  free. 
Finally,  mosquitoes  which  had  bitten  malaria  patients 
in  Rome  were  sent  to  England,  which  is  a  non-malarious 
country,  and  allowed  to  bite  two  volunteers.  Both 
contracted  malaria.  No  other  means  of  transmitting 
the  disease  has  been  discovered,  but  over  and  over 
again,  in  all  parts  of  the  world  infected  with  malaria, 
the  destruction  of  Anophehnes  has  brought  about  a 
marked  diminution  of  the  number  of  cases.  Whole 
regions,  once  scarcely  habitable,  are  now  perfectly 
healthy;  so  wonderful  is  the  effect  of  drying  up  the 
breeding-places  of  the  mosquito,  or,  if  this  be  not 
possible,  of  destroying  the  larvae  by  covering  all  Ukely 
puddles  with  oil,  which  suffocates  them.  Mosquito- 
nets  and  screens  are  an  additional  protection. 


Scientific  Discoveries  39 

(2)  Yellow  fever,  the  "Yellow  Jack"  of  our  old 
sailors,  is  a  highly  infectious,  very  dangerous  disease, 
prevalent  on  the  West  coast  of  Africa  and  in  the  West 
Indies,  and  often  occurring  in  epidemic  form  in  the 
southern  regions  of  the  United  States.  In  1905  a 
severe  outbreak  took  place  in  New  Orleans,  causing 
nine  hundred  deaths.  But  by  the  appUcation  of  a 
scientific  discovery  it  was  checked  just  at  the  time 
when  according  to  all  past  experience  it  should  have 
been  at  its  height.  Yellow  fever  was  one  of  the  greatest 
obstacles  to  the  construction  of  the  Panama  Canal,  but 
here  again  science  has  succeeded  in  wiping  out  the 
scourge.  This  discovery,  which  has  been  of  such 
enormous  practical  value,  well  illustrates  the  method 
by  which  experiments  decide  between  two  rival 
hypotheses. 

During  the  American  occupation  of  Cuba  the 
disease  became  very  prevalent  in  the  island,  and  a 
board  of  four  doctors.  Reed,  Carroll,  Lazear  and 
Agramonte,  was  appointed  in  1900  to  study  the  disease 
in  Havana.  At  the  time  there  were  two  theories  as 
to  the  transmission  of  yellow  fever.  The  dominant 
one  was  that  bedding,  clothing  and  so  forth,  which 
had  been  exposed  to  the  excreta  or  vomit  of  a  sufferer, 
spread  the  disorder.  The  other  was  that  a  mosquito, 
Stegomyia  calopus  (fasciata),  causes  it  by  biting  first 
an  infected  person  and  then  a  healthy  person.  The 
latter  theory  was  supported  by  the  very  similar  case 
of  malaria,  which  in  1898  was  shown  to  be  due  to  the 
bite  of  another  kind  of  mosquito.  In  order  to  test 
this  hypothesis  certain  people,  one  of  whom  was  Dr 
Carroll,  allowed  themselves  to  be  bitten  by  mosquitoes 
which  had  previously  fed  upon  yellow-fever  patients. 


40     Notable  Examples  of  Scientific  Discoveries 

Three  days  after  being  bitten  Dr  Carroll  sickened  and 
nearly  died ;  another  member  of  the  board,  Dr  Lazear, 
was  accidentally  bitten  and  contracted  the  disease  with 
fatal  results.  These  preUminary  experiments  en- 
couraged the  investigators  to  apply  yet  more  stringent 
tests.  An  experimental  sanitary  station,  called  Camp 
Lazear  after  the  martyr  to  science,  was  estabhshed 
in  an  open  field  near  Quemados.  Here  were  built  two 
rooms,  each  14  by  20  feet  in  size,  known  respectively 
as  the  "infected  clothing  building"  and  the  "infected 
mosquito  building."  The  former  was  so  constructed  that 
there  was  no  efl&cient  ventilation  and  no  mosquitoes  could 
enter.  The  latter  was  perfectly  ventilated,  and  screened 
so  as  to  keep  mosquitoes  in  it  as  well  as  to  keep  out 
others.  Through  the  middle  ran  a  mosquito-proof 
screen.  Into  the  former  building  were  brought  sheets, 
blankets  and  so  on,  soiled  by  contact  with  yellow -fever 
patients.  Three  volunteers,  who  had  never  had  the 
disease  and  so  were  non-immune,  unpacked  these 
articles,  made  beds  of  them  and  slept  in  them  for 
twenty  days.  The  experiment  was  repeated  three 
times.  No  case  of  fever  resulted.  Into  one  part  of 
"infected  mosquito  building"  were  introduced  fifteen 
mosquitoes  that  had  fed  on  patients  at  least  twelve 
days  before.  A  non-immune  exposed  himself  in  this 
room  to  the  bite  of  these  mosquitoes,  and  soon  after 
developed  the  disease.  At  the  same  time  two  other 
non-immunes  entered  the  other  compartment,  where 
they  slept  for  eighteen  nights  separated  from  the 
infected  mosquitoes  by  the  screen.  Neither  of  them 
caught  the  fever.  By  continual  experiment,  calling 
for  great  heroism  in  the  volunteers,  it  was  shown  that 
at  least  twelve  days  must  elapse  after  biting  a  patient 


Coiidiision  41 

before  a  mosquito  can  infect  a  healthy  person,  and  that 
there  is  no  other  way  of  spreading  yellow  fever  except 
by  inoculation  with  blood  from  a  patient  in  the  first 
two  or  three  days  of  the  disease.  The  minute  organism 
causing  the  disease  has  never  yet  been  isolated.  It  is 
too  small  for  our  microscopes  to  detect. 

Conclusion. 
Such  in  outline  is  the  method  of  discovery,  to  call 
induction  by  a  more  graphic  and  significant  name. 
By  means  of  it  scientists  are  rapidly  increasing  their 
control  over  the  forces  of  nature,  and  their  recent 
successes  appear  little  short  of  miraculous.  Sometimes 
a  success  is  the  result  of  a  brilliant  guess,  more  often 
it  is  the  outcome  of  much  careful  toil.  In  many  cases 
a  large  band  of  workers  is  set  to  attack  one  problem. 
Each  little  portion  is  assigned  to  one  scientist  or  per- 
haps to  two.  After  doing  the  task  assigned  to  him, 
which  probably  involves  a  vast  amount  of  observation 
and  experimenting,  the  research  student  writes  a  full 
account  of  his  work  and  the  conclusions  he  has  reached. 
Other  skilled  scientists  consider  the  various  reports 
and  try  to  combine  them  into  a  harmonious  whole. 
Very  often  fresh  research  is  shown  to  be  necessary  by 
this  first  examination  of  results.  Finally,  however,  if 
all  goes  well  a  definite  conclusion  is  reached,  and  the 
new  discovery  may  perhaps  bring  untold  rehef  to  man- 
kind by  stamping  out  a  dangerous  and  painful  disease. 

Deduction. 
For  centuries  deduction  was  regarded  as  by  far  the 
most  important  part  of  logic.     It  was  studied   and 
elaborated  with  the  utmost  care,  and  it  was  considered 


42  Deduction 

to  be  the  chief  instrument  in  the  acquisition  of  know- 
ledge. Aristotle,  who  first  laid  down  the  rules  for 
correct  syllogisms,  was  thought  to  be  the  supreme 
authority  in  the  art  of  reasoning,  whose  supremacy 
it  was  impious  to  question.  With  the  rise  of  modern 
science,  the  object  of  which  is  discovery,  induction 
grew  in  importance  and  deduction  fell  into  disfavour. 
The  exaggerated  importance  attached  to  deduction 
and  its  subtle  niceties  now  made  the  pendulum  swing 
too  far  in  the  opposite  direction,  and  resulted  in  undue 
disparagement.  It  was  a  long  time  before  it  was 
reaUzed  that  each  had  its  own  function  and  that 
neither  was  complete  without  the  other.  It  was  per- 
haps a  loss  that  deduction  was  over-systematized.  The 
minute  rules  for  the  construction  of  valid  syllogisms 
tended  to  make  reasoning  mechanical  and  hfeless, 
besides  obscuring  its  essential  nature.  The  main 
principle  of  deductive  reasoning  is  simple  and  easy  to 
understand.  It  is  briefly  this.  Whatever  is  true  of 
a  class  is  also  true  of  every  member  of  that  class.  If, 
for  example,  it  be  true  that  all  animals  die,  and  also 
that  X  is  an  animal,  we  may  be  certain  that  X  will 
die  sooner  or  later.  It  is  obvious  that  generahzations 
like  "all  animals  die"  are  all  discovered  by  induction, 
and  that  deduction  merely  enables  us  to  make  full  use 
of  such  discoveries. 

This  is  nearly  all  it  is  necessary  to  know  about 
deductive  reasoning,  formal  specimens  of  which  are 
called  syllogisms.  A  syllogism  consists  of  three  parts, 
called  respectively  major  premise,  mi7ior  premise  and 
conclusion.  The  most  important  kind  of  syllogism  is 
technically  known  as  Figure  I.  In  it  the  major  pre- 
mise is  always  a  general  or  universal  statement;    the 


Deduction  43 

minor  premise  may  be  either  universal  or  particular; 
the  conclusion  can  be  universal  only  if  both  premises 
are  universal. 

The  following  are  specimens  of  syllogisms. 

(1)  All  animals  are  mortal. 
All  men  are  animals. 
Therefore  all  men  are  mortal. 

(2)  No  gas  is  hghter  than  hydrogen. 
Oxygen  is  a  gas. 

Therefore  oxygen  is  not  Ughter  than  hydrogen. 

(3)  All  plums  have  stones. 
These  fruits  are  plums. 
Therefore  these  fruits  have  stones. 

If  the  general  principle  of  the  syllogism  be  thoroughly 
understood  there  is  little  need  to  learn  the  technicalities 
with  which  deductive  reasoning  has  been  overlaid,  but 
there  are  a  few  rules  and  bits  of  terminology  which  may 
prove  useful. 

Statements  or  expressions  of  judgments  are  called 
by  logicians  propositions,  and  strictly  consist  of  two 
terms  united  by  the  verb  "to  be"  called  the  copula. 
The  term  which  occurs  in  both  premises,  but  not  in  the 
conclusion,  is  called  the  middle  term.  The  subject  of 
the  conclusion  is  the  minor  term ;  the  predicate  of  the 
conclusion  is  the  major  term.  A  term  is  distributed 
when  we  make  a  statement  about  all  things  which  can 
be  included  under  the  term. 

Two  Rules  of  Quality. 

(1)  For  an  affirmative  conclusion,  both  premises 

must  be  affirmative. 

(2)  For  a  negative  conclusion,  the  premises  must 

be  opposed  in  quality. 


44  Deduction 

Two  Rules  of  Distribution. 

(1)  The  middle  term  must  be  distributed  in  one 

at  least  of  the  premises, 

(2)  Neither  extreme  term  must  be  distributed  in 

the  conclusion  unless  it  is  distributed  in 
its  premise. 
Failure  to  observe  these  rules  results  in  fallacies, 
of  which  a  good  example  is : — 
All  sugar  is  sweet. 
All  glycerine  is  sweet. 
Therefore  all  glycerine  is  sugar. 
The  middle  term  "sweet"  is  not  distributed,  and 
the  syllogism  is  a  fallacy.      But  a  much  better  way 
to  detect  the  fallacy  is  to  examine  carefully  what  the 
propositions  really  mean,  and  so  find  out  where  the 
error  lies.     Now  it  will  be  seen  that  sweetness  is  a 
very  wide  term,  and  sweet  things  may  include  sugar, 
glycerine,  saccharine  and  many  other  substances.     It  is 
therefore  not  legitimate  to  infer  that  because  things  are 
sweet  they  are  necessarily  the  same.     We  might  express 
the  facts  by  circles,  each  circle  denoting  a  term,  thus : — 


Analogy  46 

Although  the  circle  marked  "sweet  things"  includes 
the  circles  marked  "glycerine"  and  "sugar,"  the  two 
latter  for  all  we  know  do  not  overlap,  and  we  must  not 
infer  that  glycerine  is  sugar. 

Syllogisms  should  be  examined  in  this  way,  which 
is  much  better  than  trusting  to  mechanical  rules, 
however  useful  these  may  be  as  occasional  tests. 

Analogy. 

By  arguing  from  analogy  is  meant  concluding  that 
because  two  things  are  alike  in  one  or  more  than  one 
respect  they  are  also  alike  in  another  respect  or 
in  other  respects.  In  the  rough  and  tumble  of  every- 
day life  we  are  compelled  to  make  constant  use  of 
analogy  and  to  act  upon  the  conclusions  it  suggests. 
But  our  being  compelled  to  use  it  is  no  reason  why  we 
should  shut  our  eyes  to  its  dangers.  We  ought  never 
to  argue  from  analogy  without  realizing  the  inherent 
uncertainty  of  the  process. 

Children  often  make  funny  blunders  owing  to  the 
hold  analogy  has  upon  their  minds.  They  know,  for 
instance  that  the  plural  of  house  is  Jiouses,  and  they 
go  on  to  infer  that  the  plural  of  mouse  is  mouses. 

Analogy  is  justifiable  when  the  resemblance  between 
the  two  things  compared  is  very  close,  and  if  besides 
it  is  remembered  that  any  inference  drawn  is  nothing 
more  than  a  possible  or  probable  hypothesis.  Many 
scientists  are  of  opinion  that  there  is  life  on  the  planet 
Mars.  It  is  so  like  our  Earth  in  many  respects  that 
there  is  no  reason  to  doubt  that  all  the  conditions 
necessary  for  life  are  present.  But  we  cannot  regard 
the  question  as  proved.  It  remains,  and  seems  likely 
to  remain,  a  probable  hypothesis. 


46  Fallacies 

When  we  generalize,  we  frame  our  hypothesis  on 
the  close  resemblance  of  many  things  in  perhaps  only 
one  respect.  In  arguing  from  analogy,  on  the  other 
hand,  we  generally  frame  a  hypothesis  on  the  resem- 
blance of  two  things  in  several  respects.  There  is  thus 
a  close  resemblance  between  analogy  and  induction. 

Fallacies. 

A  fallacy  is  a  piece  of  reasoning  which  appears  to 
be  correct  but  really  is  not  so.  A  plajrful  instance  of 
a  fallacy  is  the  following  syllogism. 

Every  cat  has  one  more  tail  than  no  cat. 

No  cat  has  two  tails. 

Therefore  every  cat  has  three  tails. 

In  form  the  argument  is  quite  correct ;  the  explana- 
tion of  the  fallacy  is  that  the  term  "no  cat"  in  the 
major  premise  does  not  mean  the  same  thing  as  the 
term  "no  cat"  in  the  minor  premise.  As  men  every 
day  of  their  lives  reason  about  a  hundred  matters  so 
rapidly  that  the  stages  of  thought  are  slurred  over  or 
even  omitted  entirely,  it  is  not  surprising  that  fallacies 
are  constantly  occurring.  They  are  of  many  kinds,  and 
I  can  describe  only  a  few  of  them. 

Fallacies  of  the  type  given  above,  caused  by  a  term 
having  two  meanings,  are  called  fallacies  of  equivo- 
cation. The  most  interesting  of  the  other  types  are 
generally  known  by  their  Latin  names,  which  are: 
ignoratio  denchi,  or  irrelevant  conclusion ;  petitio  prin- 
cipii,  or  begging  the  question ;  post  hoc,  ergo  propter  hoc, 
or  fallacy  of  false  cause ;  nan  sequitur,  or  fallacy  of  the 
consequent. 

If  an  advocate  cannot  prove  that  his  chent  did  not 
commit  the  theft  of  which  he  is  accused,  and  so  spends 


Fallacies  47 

his  time  in  showing  what  a  brave  soldier  and  excellent 
father  he  has  been,  the  facts  stated  may  all  be  quite 
correct,  but  they  are  not  "to  the  point,"  and  the 
advocate  is  guilty  of  ignoratio  elenchi. 

Begging  the  question  is  assuming  the  point  which 
has  to  be  proved.  A  very  common  form  of  this  fallacy 
is  to  let  our  likes  and  dislikes  determine  our  notions  of 
right  and  wrong,  which  begs  the  whole  question  of  the 
nature  of  good  and  evil.  Suppose  a  man  is  trying  to 
prove  that  alcohol  is  not  injurious.  He  might  urge  that 
"it  never  did  X  any  harm."  If  this  statement  is 
founded  on  scientific  evidence  that  would  satisfy  a 
critical  board  of  medical  men,  it  is  valid  testimony, 
although  by  itself  it  is  insufficient  to  prove  the  point 
at  issue ;  but  if  it  is  merely  a  hasty,  ill-considered 
remark,  the  speaker  is  obviously  begging  the  question. 

One  of  the  commonest  fallacies  is  to  imagine  that 
post  hoc  (after  this)  necessarily  implies  propter  hoc  (on 
account  of  this).  A  misfortune  happens  to  occur  or  to 
be  heard  of  the  day  after  a  bad  dream.  The  dreamer, 
unless  he  be  very  strong-minded,  is  Ukely  enough  to 
conclude  that  the  one  caused  the  other,  or  at  any  rate 
that  the  two  incidents  are  causally  connected  in  some 
way.  To  hold  that  an  attack  of  sickness  is  due  to  one's 
last  meal  may  be  reasonable  if  the  view  be  held  merely 
as  a  hypothesis ;  to  say  that  the  meal  must  be  the 
cause  is  to  be  guilty  of  a  bad  fallacy,  unless  indeed 
there  be  other  evidence  than  the  bare  fact  that  it 
preceded  the  attack. 

A  non  sequitur  is  committed  when  a  conclusion  is 
drawn  which  does  not  follow  from  the  premises.  It 
is  really  a  faulty  syllogism,  and  in  a  way  all  faulty 
syllogisms  are  fallacies,  although  the  name  is  usually 


48  Reason  and  Authority 

applied  only  to  such  syllogisms  as  appear  to  be  correct 
in  spite  of  their  faultiness.  The  following  is  an  instance 
of  a  nan  sequitur. 

No  grasses  are  poisonous. 

This  is  grass. 

Therefore  it  Avill  make  bread. 
It  is  legitimate  to  argue  that  the  grass  in  question 
is  harmless,  but  we  cannot  properly  infer  that  its  seeds 
will  make  anything  worthy  of  the  name  of  bread. 

Reason  and  Authority. 

Everyone  ought  periodically  to  ask  himself  in  what 
way  or  ways  he  is  acquiring  fresh  knowledge.  It  is 
impossible  to  go  through  the  whole  process  on  every 
occasion,  but  the  practice  should  be  regular  and  sys- 
tematic. We  will  take  a  few  instances.  How  do  we 
learn  that  one  of  the  commonest  ways  of  expressing 
purpose  in  Latin  is  by  the  use  of  ut  and  the  subjunctive  ? 
One  way  is  to  get  the  information  from  a  grammar 
book.  If  we  do  so  we  take  the  statement  on  trust, 
there  being  no  reason,  in  all  probability,  to  doubt  the 
word  of  the  writer.  But  how  did  the  writer  acquire 
his  knowledge  ?  Perhaps  from  another  grammar  writer, 
in  which  case  he  too  took  his  information  on  trust. 
Obviously,  however,  somebody  or  other  discovered  the 
rule  by  the  process  of  induction,  and  it  is  quite  possible 
for  us  to  discover  it  in  the  same  way.  We  may,  for 
instance,  in  the  course  of  our  reading  of  Latin  notice 
that  ut  and  the  subjunctive  are  used  in  a  sentence  which 
clearly  expresses  purpose.  Later  on  we  notice  the 
same  phenomenon,  perhaps  several  times.  So  we 
frame  the   hypothesis  that  purpose   is,   at  any  rate 


Reason  and  Authority  49 

sometimes,  expressed  in  this  way.  This  hypothesis 
is  tested  again  and  again  in  the  course  of  our  reading. 

Let  us  take  an  example  from  history.  How  do 
we  know  that  the  Spanish  Armada  was  defeated  in 
the  year  1588?  Nobody  now  aUve  could  have  seen 
the  battle,  and  so  it  is  necessary  to  rely  upon  the 
testimony  of  documents.  The  evidence  of  these  has 
been  sifted  many  times  by  competent  historians,  and 
a  fairly  reUable  account  of  the  fighting  has  been  thus 
drawn  up.  It  doubtless  contains  a  few  errors  of  detail, 
but  the  general  outlines  of  the  story  are  reasonably 
certain.  These  outlines  are  given  in  the  school  text- 
books, from  which  our  knowledge  is  usually  derived. 

In  geometry  we  assume  certain  propositions  as 
self-evident  and  from  them  deduce  certain  conclusions. 
These  conclusions  we  use  as  premises  from  which  to 
deduce  other  conclusions.  In  this  way  a  whole  science 
is  built  up.  Nothing  is  taken  on  trust ;  every  step 
is  understood  and  commands  our  intellectual  assent. 
That  the  three  angles  of  every  triangle  are  equal  to 
two  right  angles  is  a  proposition  which  cannot  be  denied 
by  anyone  who  has  assented  to  the  definitions  and 
axioms  which  are  the  foundation  of  the  science  of 
geometry. 

In  studying  the  natural  sciences  we  use  both  in- 
ductive and  deductive  reasoning,  while  to  a  certain 
extent  we  rely  upon  the  authority  of  experts.  But 
the  statements  of  these  experts  can  always  be  tested 
by  students  who  have  sufficient  knowledge  and  skill 
to  make  the  necessary  experiments.  If  we  are  told 
that  conditions  X,  Y ,  and  Z  produce  result  A,  we  can 
always  appeal  to  nature  to  see  if  it  really  be  so.  This 
statement  is  not  invalidated  by  the  fact  that  only 

J.  4 


60  Reason  and  Authority 

trained  investigators  can  in  certain  cases  conduct  the 
experiments  required  to  prove  the  point. 

When,  therefore,  you  ask  yourself  how  you  obtain 
a  fresh  piece  of  knowledge,  first  of  all  inquire  how  far 
you  are  relying  upon  your  own  reason,  and  how  far 
upon  the  authority  of  others.  It  may  be  that  the 
question  of  authority  does  not  come  in  at  all,  but  if  it 
does,  go  on  to  ask  whether  it  is  possible  to  apply  the 
test  of  an  appeal  to  reahty.  If  it  is  possible,  applj^  it 
yourself,  or  at  least  find  out  whether  others  have 
appUed  it  already;  but  if  it  is  not  possible  (as  for 
instance  in  the  case  of  many  history  problems)  you 
must  take  steps  to  estimate  the  credibility  of  your 
authority,  remembering  that  no  absolutely  certain 
conclusion  can  be  reached.  The  question  is  one  of 
greater  or  less  probability. 

The  testing  of  authority  by  an  appeal  to  reality 
is  well  illustrated  by  the  research  of  a  mathematician 
named  John  Adams,  who  was  afterwards  a  famous 
astronomer.  When  quite  a  young  man  he  was  puzzled 
by  the  strange  and  irregular  movements  of  the  planet 
Uranus.  The  hypothesis  occurred  to  him  that  there 
might  be  another  planet,  unknown  to  astronomers, 
which,  by  the  attractive  force  which  all  bodies  exert, 
was  influencing  the  movements  of  Uranus.  He  pro- 
ceeded to  make  calculations  as  to  the  probable  direction 
in  which  this  planet  could  be  observed,  and  concluded 
that  in  a  certain  spot  a  planet  of  a  certain  size  would 
be  seen  by  the  help  of  a  sufficiently  powerful  telescope. 
He  wrote  to  Greenwich  asking  the  Astronomer  Royal 
to  verify  his  hypothesis,  but  as  he  was  an  unknown 
man  his  request  was  ignored.  Some  time  later  a 
French  astronomer  came  to  the  same  conclusion  as 


Additional  Note  51 

to  an  unknown  planet.  Being  more  fortunately 
situated  than  Adams  he  was  able  to  apply  the  simple 
test  of  "look  and  see,"  and  so  discovered  the  planet 
Neptune. 

ADDITIONAL  NOTE. 

In  this  Uttle  book  I  have  used  the  word  hypothesis 
to  denote  any  interpretation  of  phenomena,  however 
simple  or  however  complex  that  interpretation  may  be. 

You  will  notice  that  these  interpretations  are  of  at 
least  three  different  kinds. 

( 1 )  They  may  result  in  particular  propositions,  e.g. : 
That  is  an  apple. 

The  disease  that  he  is  suffering  from  is  influenza. 

(2)  They  may  result  in  general  propositions  of  such 
a  kind  that  every  instance  can  be  examined  and  brought 
under  the  general  rule,  e.g. : 

Ut  meaning  in  order  that  always  takes  the  sub- 
junctive in  Latin.  (Every  instance  of  this  construction 
in  Latin  hterature  has  been  noted  and  examined.) 

(3)  They  may  result  in  general  propositions  of  such 
a  kind  that  every  instance  cannot  be  examined,  e.g. : 

All  animals  require  food.  (This  statement  is  true 
so  far  as  we  know,  but  some  day  science  may  possibly 
discover,  perhaps  in  another  planet,  animals  which  do 
not  require  food  to  maintain  life.) 

Some  logicians  use  the  word  hypothesis  in  a  narrower 
sense,  and  you  must  not  allow  this  lack  of  uniformity  to 
cause  confusion  in  your  mind  when  you  are  reading 
other  text-books. 


4—2 


APPENDIX 

EXAMPLES  OF  INDUCTIVE  REASONING 
DONE   BY  BOYS 


Problem.     Why  are  large  towns  situated  where  they 
are? 

Stage  1.     Collection. 

N.B.  Here  is  need  of  an  obvious  caution.  It  is 
impossible,  for  me  at  least,  to  collect  the  evidence  of 
all  the  towns  that  ever  were.  Many  have  long  since 
perished,  and  of  those  thousands  now  existent  we  can 
hardly  examine  more  than  a  few.  Let  us  take  then, 
roughly  speaking,  the  world's  chief  cities  as  fair  examples 
of  the  whole. 
London.     On  the   mouth   of  the  Thames.     Harbour. 

Ancient  military  position. 
Edinburgh.     On  a  mount  commanding  the  whole  neigh- 
bourhood. 
Dublin.     On  a  natural  harbour.     River. 
Paris.     On  a  navigable  river,   at  junction  with  two 

tributaries. 
Brussels.     On  small  river.    Central  position  in  kingdom. 
Amsterdam.     River  mouth. 
Berne.     Fertile  region.     Valley  (trade  route). 


Appendix  53 

Berlin.     Fertile  plain, 

Stuttgart.     Trade  valley. 

Munich.     Trade  valley. 

Breslau.     Fertile  region.     On  river. 

Warsaw.     River.     Fertile  region. 

Petrograd.     Harbour  and  river. 

Moscow.     Fertile  region.     Between  two  large  rivers. 

Vienna.     Fertile  river  valley  used  as  trade  route. 

Pest.     Where  trade  river  flows  into  fertile  plain. 

Belgrade.  Confluence  of  two  rivers.  Important  mili- 
tary position. 

Bukharest.     Central  position  in  fertile  plain. 

Sofia.     Junction  of  two  valleys.     Mountain  fastness. 

Constantinople.     Commanding    Bosphorus.     Harbour. 

Athens.     Ancient  stronghold.     Harbour. 

Scutari.     Very  fertile.     On  lake  (fishing?). 

Cettinje.     Mountain  fastness. 

Naples.     Fertile  bay.     Good  harbour.     Health  resort. 

Rome.     On  river.     Stronghold. 

Turin.     River.     Where  trade  route  enters  fertile  plain. 

Milan.     Central  position  in  fertile  plain. 

Venice.  Head  of  Adriatic,  and  at  mouth  of  trade  river. 
Lagoon  harbour. 

Lisbon.     River  and  harbour. 

Madrid.  On  commanding  position  near  long  and  wide 
river.     Fertile. 

Copenhagen.  On  island  commanding  The  Sound. 
Thus  military  and  trading  centre. 

Christiania.     River  and  harbour.     Fertile  valley. 

Stockholm.     Harbour.     Fertile  region. 

Cairo.     Mouth  of  river.     Near  fertile  delta. 

Aden.  Trade  route.  Military  position  commanding 
both  straits  and  interior. 


54  Appendix 

Calcutta.     River.     Fertile  delta  with  many  harbours. 

Madras,     River.     Mihtary  position. 

Bombay.     Harbour. 

Colombo.     Outlet  from  interior.     Harbour. 

Timbuktu.    (Where  desert  trade  route  joins  river  most 

northerly  point.)     Oasis. 
Sydney.     Harbour       \  Apparently  just  where  the  ex- 
Brisbane.     Harbour  ploring  navigator  happened 
Adelaide.     Harbour     ^         to  strike  the  coast,  which  is 
WelUngton.     Harbour  full  of  harbours   quite   as 
Dunedin.     Harbour      '         good  and  even  better. 
Perth  (W.A.),     Harbour  in  fertile  region  (two  rivers). 
Hobart.     Sheltered  harbour  (island  in  front  of  coast). 
Cape  TowTi.     Harbour  and  military  position. 
Bloemfontein.     River.     Fertile  plain. 
Pretoria.     Native  trade  centre.     River. 
Durban.     Harbour. 

Pekin.     Fertile  plain.     Between  two  great  rivers. 
Seoul.     Near  harbour.     Only  large  river  from  interior. 
Tokio.     Harbour. 

Kioto.     On  lake  surrounded  by  hills.     ( ?Fertility.) 
Sparta.     Military  position. 

Thebes.     Fertile  plain.     River.     Military  position. 
Amphipohs.     Harbour.     Outlet  for  gold  trade. 
Tegea.     Fertile  plain. 
Kimberley.     Mines, 
Brighton.     Health  resort, 

c  ,      .    f  Isthmus  on  trade  route, 
fey  bans.  J 

Carthage.     Harbour.     Mihtary  position. 

Nineveh.  I  Trade  route  (river).     Fertile  compared  to 

Babylon.  [  desert. 

Mycenae.    Harbour.    Military  position.    Fertile  region. 


Appendix  55 

Stage  2.     Arranging. 

I.  Trade  Route: — Paris,  Stuttgart,  Munich, 
Pretoria,  Corinth,  Sybaris.  6 

II.  Harbours : — Bombay,  Sydney,  Brisbane,  Ade- 
laide, Wellington,  Hobart,  Dunedin,  Durban, 
Tokio.  9 

III.  Fertility^: — Berlin,  Scutari,  Tegea,  Kjmber- 

ley,  Kioto  (?).  5 

IV.  Military  Position  : — Edinburgh,  Cettinje.  2 
V.   Central  Position: — Brussels.  1 

VI.  Health  Resort: — Brighton.  1 

24 

I  and  II : — London,  Dublin,  Amsterdam,  Petro- 
grad,  Constantinople,  Venice,  Lisbon,  Colom- 
bo, Seoul,  Amphipolis.  10 

I  and  III : — Berne,  Breslau,  Warsaw,  Moscow, 
Vienna,  Pest,  Turin,  Madrid,  Cairo,  Tim- 
buktu, Bloemfontein,  Pekin,  Nineveh,  Baby- 
lon. ^         14 

I  and    IV : — Sofia,    Rome,    Copenhagen,    Aden, 

Madras,  Sparta.  6 

II  and  III :- Stockholm,  Perth  (W.A.)  2 

II  and  IV : — Athens,  Cape  Town,  Carthage.  3 

III  and  V :— Bukharest,  Milan.  2 

37 
I,  II  and  III : — Christiania,  Calcutta.  2 

I,  III  and  IV :— Belgrade,  Thebes.  2 

II,  III  and  IV:— Mycenae.  1 
II,  III  and  VI :— Naples.  1 

6 

^  This  is  meant  to  include  all  natural  resources  and  riches  of 
the  land,  as  mines,  etc. 


56  Appendix 

Stage  3.     Inferences. 

1.  There  are  six  main  reasons  for  the  situation  of 
towns :  trade  routes,  harbours,  fertihty,  military 
position,  central  position,  health. 

2.  Most  towns  are  built  with  a  view  to  two  of  the 
above  reasons,  except  Australian  towns,  springing  up 
merely  because  they  happened  first  to  give  shelter 
to  the  exploring  navigator. 

3.  There  is  httle  or  no  evidence  of  the  element  of 
chance,  except  in  so  far  as  harbours  were  apparently 
chosen  indiscriminately  on  a  coast  rich  in  them. 

Stage  4.    Tentative  Hypothesis. 

All  towns  are  situated  either  on  trade  routes,  or 
on  harbours,  or  in  fertile  regions,  or  in  positions  of 
military  or  naval  importance,  or  in  central  positions 
convenient  for  exercising  surveillance  over  a  district, 
or  in  a  particularly  bracing  spot  for  the  purpose  of 
recreating  health ;  but  generally  towns  are  founded 
with  a  view  to  two  or  more  of  these  functions. 

Stage  5.    Testing. 

Manchester.   Explained  by  III  and  V )  surveillance  over 

Leeds.  „  III  and  V  j     smaller  towns. 

Sheffield.  „  III,  (?V). 

Orleans.  „  III,  I. 

New  York.  „  II,  I. 

Quebec.  ,,  II,  I. 

Port  Elizabeth.  „  II,  I,  (?III). 

Washmgton.  „  V,  II,  I,  (III?). 

New  Orleans.  ,,  I,  III. 


Aijpendix 


57 


Chicago.       Explained 

Prague. 

Larissa. 

Salonika. 

Sm3n:Tia. 

Kiev. 

Konigsberg, 

Riga. 

Sevastopol. 

Adrianople. 

Klausenburg. 

Quito. 

La  Paz. 

Panama. 

Monte  Video. 

Rio  de  Janeiro. 

Santa  Cruz. 

Valparaiso. 

Irkutsk. 

Blackpool. 

Nice. 

Spa. 


by  I. 

I,  IV,  V,  (III?). 

III,  V. 
I,  II. 

I,  II,  III,  IV,  V. 

I,  V,  (III?). 

II,  I,  IV. 

I,  II,  III,  IV,  V,  VI. 

II,  III,  IV,  VI. 

IV,  I,  III. 

V,  III. 

Ill  (mines),  IV. 

IV,  III  (mines). 

I. 

II,  IV. 

II,  V. 

II,  (III?). 

V  (as  port  to  Santiago),  II. 

II,  V,  (IV?),  (III?). 

VI. 

VI. 

VI. 


BUT 

r  Jerusalem. 


Bury  St  Edmunds. 

Ely. 

Cambridge. 


Though  partly  IV,  III,  V,  yet 
partly  because  of  reUgious 
interest. 

Solely  because  of  abbey. 

Though  partly  IV,  V,  III,  II,  yet 
largely  because  of  cathedral. 

Though  partly  IV,  I,  V,  yet 
largely  from  educational  in- 
terest. 


58  Appendix 

Stage  6,     Emending. 

Thus  the  hypothesis  falls  through,  or  at  least  has 
to  be  emended.     Thus  we  finally  arrive  at 

Stage  7.     Final  Hypothesis. 

All  towns  are  situated  either  on  trade  routes,  or 
harbours,  or  in  fertile  regions,  or  positions  of  miUtary 
or  naval  importance,  or  in  central  positions  convenient 
for  exercising  surveillance  over  a  district,  or  in  a  parti- 
cularly bracing  spot,  or  at  a  locality  of  pecuUar  rehgious 
or  other  such  interest  or  importance ;  but  generally 
towns  are  founded  with  a  view  to  at  least  two  of  these 
functions. 

II. 

Problem.  What  are  the  facts  which  determine  the 
markings  and  colours  of  freshwater  fish  ? 

Evidence.  Let  us  examine  the  markings  of  the 
following  fish,  and  try  to  see  the  use  of  them  : — 

(a)  The  pike.  Coloured  dark  green  with  shading 
on  the  back,  hght  green  and  white  underneath.  He 
swims  chiefly  in  mid  water,  and  eats  small  fish,  living 
both  on  the  bottom  and  on  the  surface.  His  markings 
render  him  almost  invisible  from  above  or  below. 

(6)  The  trout  lives  often  in  clear  streams  and  his 
spotted  skin  thus  enables  him  to  be  almost  invisible 
to  his  great  enemy,  man,  against  the  gravel  bottom. 

(c)  The  roach  lives  chiefly  on  the  bottom,  and  is 
coloured  either  dark  green,  brown,  or  black  according 
to  the  locahty,  and  white  underneath.  His  big  enemy 
the  pike  nearly  always  attacks  from  above ;  and  it  is 
from  here  that  he  is  most  invisible. 


Appendix  59 

{d)  The  perch  lives  in  streams  with  sandy 
bottoms,  against  piles  and  other  such  things.  His 
brown  and  black  striped  back,  while  he  is  white  under- 
neath, renders  him  almost  invisible  to  the  small  fish 
that  form  his  prey. 

(e)  The  dace  lives  either  on  the  bottom  or  the 
surface ;  is  coloured  black  or  dark  green  accordingly  on 
the  back,  and  is  a  bright  silvery  colour  underneath. 
His  enemies,  the  pike  and  the  perch,  both  attack  from 
below  him  when  he  is  on  the  surface,  but  his  colour 
protects  him  well. 

(I  know  I  am  liable  to  err  here  owing  to  my  limited 
knowledge  of  the  habits  of  fish,  and  total  ignorance  even 
of  the  existence  of  some  small  species.) 

Classification.  Most  freshwater  fish  are  similar  to 
one  of  the  species  described  above.  Then  we  may 
classify  as  follows;  (i)  Fish  which  take  the  colour  of 
their  surroundings  to  capture  their  prey,  (ii)  Those 
which  do  so  to  escape  from  their  enemies.  We  now 
frame  our  hypothesis  : — 

Hypothesis.  Freshwater  fish  have  their  colour  in- 
fluenced by  their  surroundings  and  habits  with  a  view 
to  (i)  escape  from  their  enemies;  (ii)  catching  their 
prey. 

Testing.  We  now  try  to  prove  this  by  seeing  how 
the  habits  and  colour  of  other  fish  fit  it. 

(1)  Bream  is  a  bottom-feeding  fish,  subject  to 
attacks  from  pike.     It  is  therefore  dark-coloured. 

(2)  Tench  and  carp  are  rather  similar.  They  live 
on  the  bottom  and  are  therefore  dark-coloured,  to 
protect  them  from  the  pike. 

(3)  Bleak  is  a  surface  fish  with  habits  and 
markings  similar  to  the  dace. 


60  Qtiestions 

(4)  Gudgeon  lives  on  gravel  or  muddy  bottom  and 
is  more  or  less  muddy  coloured  with  spots,  according 
to  the  locahty. 

Thus,  none  of  these  fish  being  contrary  to  the 
hypothesis,  this  hypothesis  is  so  far  correct. 

Among  the  fish  I  have  omitted  to  mention  are : — 
chub,  rudd,  char,  loach,  minnow,  grayling  and  barbel. 

QUESTIONS 
A. 

(1)  Give  six  examples  of  the  way  in  which  the  mind  interprets 
impressions  presented  to  it  by  the  senses. 

(2)  Give  three  examples  of  sense-impressions  misinterpreted  by 
the  mind. 

(3)  Expand  the  statement  that  thoughts  are  judgments  about 
sense-impressions. 

(4)  Illustrate  the  part  played  by  experience  in  the  interpreta- 
tion of  sense-impressions. 

(5)  What  is  the  relation  of  science  to  our  sense-impressions? 

(6)  Illustrate  the  difference  between  formal  logic  and  scientific 
method. 

B. 

(1)  What  is  the  relation  between  the  meaning  of  a  word  to  us 
and  our  past  experience? 

(2)  How  do  we  learn  to  use  words  more  accurately? 

(3)  Why  is  it  important  to  eUminate  our  own  peculiar  notions 
as  to  the  meanings  of  words  ? 

(4)  What  kinds  of  words  are  most  difficult  to  define,  and  why? 

(5)  What  is  meant  by  a  logical  definition? 

(6)  What  is  the  value  of  the  power  to  define  correctly? 


Questions  61 

(7)  Is  it  possible  to  define  the  following  ? 

(a)  Julius  Caesar. 

(6)  Dogs. 

(c)  Water. 

(d)  Wheat, 
(c)  Latin. 

(/)     British  Museum. 

ig)     Being. 

Give  your  reasons  in  all  cases.  If  a  thing  cannot  be  defined,  how 
can  it  be  made  known  to  others  by  means  of  language  ? 

(8)  What  is  a  synonym?     Give  examples. 

(9)  What  is  the  value  of  precision  in  the  use  of  language  ?  Give 
some  reasons  why  such  precision  is  diificult. 

(10)  State  in  your  own  words  the  virtues  and  the  defects  of 
language  as  a  means  of  expressing  thought. 

(11)  Give  some  reasons  why  it  is  difficult  to  impart  truth  to 
others  by  means  of  language. 

C. 

(1)  Illustrate  the  difference  between  deduction  and  induction. 

(2)  WTiat  are  the  essential  parts  of  a  piece  of  inductive  reasoning  ? 

(3)  State  any  problem,  and  indicate  the  steps  by  which  you 
would  solve  it  by  induction. 

(4)  Illustrate  by  examples  the  danger  of  hasty  generalization. 

(5)  What  is  meant  by  a  working  hypothesis? 

(6)  What  ought  our  attitude  to  be  towards  a  hypothesis? 

(7)  What  quahties  are  required  in  a  scientific  worker? 

(8)  What  exactly  is  meant  by  an  experiment? 

(9)  In  testing  a  hypothesis  by  experimentation  what  precaution 
should  be  observed  ? 

(10)  What  is  meant  by  evidence?  Illustrate  by  examples  the 
various  kinds  of  evidence  that  present  themselves  in  the  solution  of 
problems. 


62  Questions 

(11)  What  should  be  our  attitude  towards  testimony  which 
cannot  be  tested  by  experimentation? 

(12)  How  should  we  estimate  the  probabihty  of  a  piece  of 
testimony  of  the  kind  mentioned  in  question  11? 

(13)  Illustrate  from   everyday  life   the  weighing   of   evidence 
and  the  estimating  of  probabihties. 

(14)  Why  is  classification  an  important  part  of  scientific  work? 

(15)  Give  examples  of  (a)  correct  and  (6)  incorrect  classification. 

(16)  Give  a  rough  classification  of  the  sciences.     Why  is  it 
impossible  to  classify  them  with  perfect  accuracy? 

(17)  Why  are  new  sciences  constantly  arising? 

(18)  What  is  meant  by  a  syllogism? 

(19)  What  is  the  main  principle  of  syllogistic  reasoning? 

(20)  What  are  the  essential  parts  of  a  syllogism? 

(21)  State  the  main  rules  of  the  syllogism. 

(22)  Why  is  it  unwise  to  follow  blindly  these  rules? 

(23)  Why  has  deductive  logic  fallen  into  disfavour  during  the 
last  two  centuries  or  so? 

(24)  Explain  how  syllogisms  can  be  illustrated  by  combinations 
of  circles. 

(25)  What  is  meant  by  analogy?     Show  how  apt  it  is  to  influ- 
ence our  everyday  reasoning. 

(26)  Explain  what  is  meant  by  a  fallacy,  and  describe  the  most 
common  types  of  fallacy. 

(27)  Express  as  formal  syllogisms  the  following  arguments. 
Which  arguments  are  fallacious,  and  why  ? 

(o)     It  will  rain  to-morrow,  because  the  moon  has  a  halo. 
(6)     There  must  be  pepper  in  this  soup,  it  is  so  hot. 

(c)  The  doctor's  motor  is  outside  ^'s  house.     Somebody  must 
be  ill  there. 

(d)  This  hquid  is  acid.     It  turns  blue  Utmus  red. 

(e)  I  must  use  ut  in  turning  this  sentence  into  Latin,  as  it 
expresses  purpose. 


Questions  63 

(/)     Richard  the  First  was  a  good  king,  because  he  fought  well. 

(g)     Why  do  you  sigh?     You  have  not  lost  a  fortune. 

{h)     She  drinks  strong  tea.     Her  nerves  must  be  weak. 

(i)     X  must  be  ill,  as  he  has  not  written  for  three  days. 

(j)     You  ought  to  wear  thicker  clothes,  for  it  is  very  cold. 

(k)     You  cannot  be  really  well,  for  you  do  not  eat  proper  food. 

(/)      The  Prime  Minister  is  wrong;    The  Times  says  so. 

(to)    This  body  will  not  fall,  for  its  centre  of  gravity  is  below 
the  point  of  support. 

(n)     But  Brutus  says  he  was  ambitious. 
And  Brutus  is  an  honourable  man. 

(o)     This  figure  has  three  sides ;  therefore  its  angles  are  equal 
to  two  right  angles. 

(p)    John  is  a  bad  boy,  for  he  was  given  only  30  per  cent,  for 
his  French  this  week. 

(q)     Look  at  that  crowd.     There  must  have  been  an  accident. 

(28)  What  processes  of  thought  ought  one  to  go  through  before 
being  convinced  of  the  truth  of  the  following  pieces  of  information? 

{a)  The  Greeks  defeated  the  Persians  at  Salamis  in  the  year 
480  B.C. 

(6)  Pekin  is  the  capital  of  China. 

(c)  Bubonic  plague  is  spread  by  the  fleas  of  infected  rats. 

(d)  The  formula  of  sulphiuic  acid  is  H2SO4. 

(e)  True  synonyms  do  not  exist. 

(/)  Ut  and  the  subjunctive  in  Latin  often  express  consequence. 

(g)  Common  salt  easily  dissolves  in  water,  chalk  does  not. 

(h)  The  centre  of  gravity  of  a  sphere  is  its  centre. 

(i)  If  a  triangle  has  three  equal  sides  it  also  has  three  equal 
angles. 

(j)  "To  quickly  write"  is  not  good  English. 

(29)  Describe  the  way  in  which  the  means  of  preventing  malaria 
was  discovered. 

(30)  Describe  the  experiments  which  proved  that  yellow  fever 
is  carried  from  man  to  man  by  Stegomyia. 


64  Questions 

(31)     Outline  the  means  you  would  adopt  to  solve  the  following 
problems. 

(a)  At  what  sort  of  points  in  his  story  does  Virgil,  in  the  Aeneid, 
use  similes  ? 

(6)  What  has  been  the  effect  upon  history  of  the  invention 
of  new  weapons? 

(c)     What  are  the  best  conditions  for  the  cultivation  of  roses  ? 

{d)  What  are  the  advantages  of  brown  bread  and  white  bread 
respectively  ? 

(e)  Does  there  appear  to  be  any  connection  between  industrial 
changes  and  political  movements? 

(/)  What  is  the  difference  between  the  Latin  words  frustra 
and  nequiquam  ? 

ig)    What  causes  dew? 

{h)     How  can  a  cut  cheese  be  kept  from  going  mouldy? 


CAMBRIDGE:    PRINTED  BY  J.  B.  PEACE,  M.A.,  AT  THE  UNIVERSITY  PRESS 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 

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